diff --git a/docs/core/alerting.md b/docs/core/alerting.md
index 5ee6a14..dbfc94d 100644
--- a/docs/core/alerting.md
+++ b/docs/core/alerting.md
@@ -168,10 +168,11 @@ alert in the window, oldest first, in their own zone, with a subject like
 "[Steward] 3 alerts: 2 firing, 1 resolved". One alert on its own keeps its
 usual email.
 
-Email waits in the database (`email_outbox`, `core/outbox.py`) until the mail
-server accepts it, so nothing waiting is lost when Steward restarts: the
-sender picks it up at boot. The sender runs every 15 seconds and settles each
-email on the server's answer:
+Every email Steward sends (alerts, the weekly report, invites, password
+resets and the test buttons) waits in the database (`email_outbox`,
+`core/outbox.py`) until the mail server accepts it, so nothing waiting is lost
+when Steward restarts: the sender picks it up at boot. The sender runs every 15
+seconds and settles each email on the server's answer:
 
 - **Accepted:** sent.
 - **Refused** (an SMTP 5xx, such as "no such mailbox"): failed at once, with
@@ -183,6 +184,13 @@ email on the server's answer:
 Once every email carrying an alert has settled, that alert's event records
 whether the email went, and to whom it didn't.
 
+An email a person is waiting on is tried at once instead of on the next tick:
+the weekly report's **Send now**, an invite, and the test buttons, so the page
+can say what the server answered. A report or invite the server couldn't take
+yet stays queued and is retried as above. A test (the Settings → Notifications
+test email, a rule's **Send test**) is recorded but never retried: its one
+answer is the result.
+
 ### Webhook
 
 Configured at `/settings/` under Webhook. The body is a Jinja2 template rendered to JSON. Content-Type is always `application/json`. If the rendered template is not valid JSON, the delivery is logged as failed and no request is sent.
diff --git a/steward/alerts/service.py b/steward/alerts/service.py
index aecb2b7..a5b8b43 100644
--- a/steward/alerts/service.py
+++ b/steward/alerts/service.py
@@ -266,9 +266,9 @@ async def active_count(db) -> int:
 
 def notify_targets(smtp: dict, webhook: dict, accounts: int = 0) -> list[str]:
     """Where an alert's notifications go, in words, by the same tests
-    core.notifications.dispatch_notifications sends by: email when a server
-    is set and `accounts` (that get alerts) or Also send to addresses exist,
-    a webhook when its URL is. Empty: nobody (#5315, milestone 495)."""
+    alerts are sent by: email when a server is set and `accounts` (that get
+    alerts) or Also send to addresses exist (core.outbox.hold_alert), a
+    webhook when its URL is (core.notifications.dispatch_notifications). Empty: nobody (#5315, milestone 495)."""
     from urllib.parse import urlsplit
     out = []
     recipients = smtp.get("recipients") or []
@@ -752,7 +752,8 @@ async def send_test(app, rule_id: str) -> dict:
     failed; lines say what happened to each channel. LookupError for no rule.
     """
     from urllib.parse import urlsplit
-    from steward.core.mail import recipients
+    from steward.core import outbox
+    from steward.core.mail import alert_email, recipients
     from steward.core.notifications import dispatch_notifications
     smtp, webhook = app.config.get("SMTP", {}), app.config.get("WEBHOOK", {})
     async with app.db_sessionmaker() as db:
@@ -761,12 +762,14 @@ async def send_test(app, rule_id: str) -> dict:
             raise LookupError(rule_id)
         alert = await test_alert(db, rule)
         to = await recipients(db, "alerts", smtp) if smtp.get("host") else []
-    results = await dispatch_notifications(smtp, webhook, alert, to)
+    results = await dispatch_notifications(webhook, alert)
     lines = []
-    if email := results.get("email"):
-        who = ", ".join(r.address for r in to)
-        lines.append(f"Email sent to {who}." if email["sent"]
-                     else f"Email to {who} failed: {email['error']}")
+    if to:
+        # Queued and recorded like any email, tried once, not retried.
+        ok, said = outbox.said(await outbox.send_each(
+            app, "test", to, lambda r: alert_email(smtp, alert, r), retry=False))
+        results["email"] = {"sent": ok, "error": None if ok else said}
+        lines.append(f"Email: {said}")
     if hook := results.get("webhook"):
         host = urlsplit(webhook["url"]).hostname or webhook["url"]
         lines.append(f"Webhook to {host} delivered." if hook["sent"]
diff --git a/steward/auth/routes.py b/steward/auth/routes.py
index 8f2fd4a..066f692 100644
--- a/steward/auth/routes.py
+++ b/steward/auth/routes.py
@@ -436,7 +436,7 @@ async def forgot_post():
     accounts; every request from an address counts toward its limit."""
     from quart import current_app
     from steward.auth.throttle import reset_throttle
-    from steward.core import mail
+    from steward.core import mail, outbox
     from steward.core.audit import log_audit
     from steward.core.formatting import zone
     from steward.core.password_resets import account_for, issue, link
@@ -454,16 +454,15 @@ async def forgot_post():
             user = await account_for(db, name)
             if user is not None:
                 reset, key = await issue(db, user)
-                to, username, user_id, tz = user.email, user.username, user.id, user.time_zone
+                username, user_id = user.username, user.id
+                to = mail.Recipient(user.email, zone(user.time_zone), False, username)
+                subject, text, html = mail.reset_email(username, reset.expires_at,
+                                                       link(public_base_url(request), key), to.tz)
+                # Sent by the outbox, with the link's own transaction; the page
+                # says the same either way, and the queue records how it went.
+                outbox.enqueue(db, kind="reset", to=to, subject=subject, text=text, html=html)
     if user is None:
         return await _forgot_page(sent=True)
-    cfg = current_app.config.get("SMTP", {})
-    subject, text, html = mail.reset_email(username, reset.expires_at,
-                                           link(public_base_url(request), key), zone(tz))
-    try:
-        await mail.send(cfg, [mail.message(cfg, to, subject, text, html)])
-    except Exception as exc:                # the page still says the same; the log says why
-        current_app.logger.warning("Password reset email to %s failed: %s", to, exc)
     await log_audit(current_app, user_id, username, "user.password_reset_requested", "user", user_id,
                     detail={"address": ip})
     return await _forgot_page(sent=True)
diff --git a/steward/core/alerts.py b/steward/core/alerts.py
index e8a1bf8..f656e9f 100644
--- a/steward/core/alerts.py
+++ b/steward/core/alerts.py
@@ -522,7 +522,7 @@ async def _dispatch_notification(
             await outbox.hold_alert(app, alert_data, event_id)
         except Exception:
             logger.exception("Alert %s: its email could not be queued", event_id)
-    results = await dispatch_notifications({}, app.config.get("WEBHOOK", {}), alert_data)
+    results = await dispatch_notifications(app.config.get("WEBHOOK", {}), alert_data)
 
     webhook_r = results.get("webhook")
     if not webhook_r:
diff --git a/steward/core/mail.py b/steward/core/mail.py
index 7c65f7c..720dbac 100644
--- a/steward/core/mail.py
+++ b/steward/core/mail.py
@@ -163,13 +163,6 @@ async def audience(db) -> dict:
     return out
 
 
-async def send(cfg: dict, messages: list[EmailMessage]) -> None:
-    """Send every message over one SMTP connection, off the event loop."""
-    import asyncio
-    from steward.core.notifications import _smtp_send_sync
-    await asyncio.get_running_loop().run_in_executor(None, _smtp_send_sync, cfg, messages)
-
-
 def _render(name: str, **ctx) -> tuple[str, str]:
     ctx = {"c": palette(), **ctx}
     return (_env.get_template(f"{name}.txt").render(ctx),
diff --git a/steward/core/notifications.py b/steward/core/notifications.py
index 814fcda..62e4056 100644
--- a/steward/core/notifications.py
+++ b/steward/core/notifications.py
@@ -4,7 +4,6 @@ import logging
 import smtplib
 import ssl
 import types
-from email.message import EmailMessage
 
 import httpx
 from jinja2.sandbox import SandboxedEnvironment
@@ -12,20 +11,11 @@ from jinja2.sandbox import SandboxedEnvironment
 logger = logging.getLogger(__name__)
 
 
-async def dispatch_notifications(
-    smtp_cfg: dict,
-    webhook_cfg: dict,
-    alert_data: dict,
-    recipients: list = (),
-) -> dict:
-    """Dispatch all configured notification channels: email to each of
-    `recipients` (mail.Recipient, from mail.recipients) when a server is set.
-    Returns results dict."""
+async def dispatch_notifications(webhook_cfg: dict, alert_data: dict) -> dict:
+    """Post an alert's webhook when one is set; {"webhook": result} or {}.
+    Email goes through the outbox instead (core.outbox, #5506)."""
     results = {}
 
-    if smtp_cfg.get("host") and recipients:
-        results["email"] = await _send_email(smtp_cfg, alert_data, recipients)
-
     if webhook_cfg.get("url"):
         results["webhook"] = await _send_webhook(webhook_cfg, alert_data)
 
@@ -43,21 +33,10 @@ def smtp_mode(port, tls) -> str:
     return "starttls" if tls else "plain"
 
 
-async def _send_email(cfg: dict, alert: dict, recipients: list) -> dict:
-    """Each recipient their own copy, in their own zone, over one connection."""
-    from steward.core.mail import alert_email, message, send
-    try:
-        messages = [message(cfg, to.address, *alert_email(cfg, alert, to)) for to in recipients]
-        await send(cfg, messages)
-        return {"sent": True, "error": None}
-    except Exception as exc:
-        logger.error(f"Email notification failed: {exc}")
-        return {"sent": False, "error": str(exc)}
-
-
 def smtp_open(cfg: dict) -> smtplib.SMTP:
     """A connection to the mail server, TLS and login done, every step
-    bounded by SMTP_TIMEOUT_S. The caller closes it (use it in `with`)."""
+    bounded by SMTP_TIMEOUT_S. The caller closes it (use it in `with`).
+    Only core.outbox.deliver_sync opens one: every email is a queued row."""
     port = int(cfg.get("port") or 587)
     mode = smtp_mode(port, cfg.get("tls", True))
     ctx = ssl.create_default_context()
@@ -76,12 +55,6 @@ def smtp_open(cfg: dict) -> smtplib.SMTP:
     return smtp
 
 
-def _smtp_send_sync(cfg: dict, messages: list[EmailMessage]) -> None:
-    with smtp_open(cfg) as smtp:
-        for msg in messages:
-            smtp.send_message(msg)
-
-
 def _json_str(value) -> str:
     """A value as it may sit between the quotes of a JSON string."""
     return json.dumps("" if value is None else str(value))[1:-1]
diff --git a/steward/core/outbox.py b/steward/core/outbox.py
index 4f460d3..3d2a427 100644
--- a/steward/core/outbox.py
+++ b/steward/core/outbox.py
@@ -33,7 +33,7 @@ import logging
 import smtplib
 from datetime import datetime, timedelta, timezone
 from email.message import EmailMessage
-from typing import TYPE_CHECKING
+from typing import TYPE_CHECKING, Callable
 
 from sqlalchemy import insert, or_, select, text, update
 
@@ -104,18 +104,22 @@ def reason(exc: BaseException) -> str:
 
 def enqueue(db, *, kind: str, to: "Recipient | str", subject: str | None = None,
             text: str | None = None, html: str | None = None,
-            send_after: datetime | None = None, retry: bool = True,
+            send_after: datetime | None = None, retry: bool = True, claimed: bool = False,
             now: datetime | None = None) -> EmailOutbox:
     """Add one email to the queue in `db`'s transaction (the caller commits).
     `send_after` holds it until then (an alert burst, #5507); otherwise it is
-    due at once. `to` is a mail.Recipient, or a bare address read in UTC."""
+    due at once. `claimed` marks it as being sent by the caller, who will
+    `attempt` it right after committing, so the sender doesn't take it too;
+    a claim the caller never settles goes back to the queue (STALE_CLAIM_S).
+    `to` is a mail.Recipient, or a bare address read in UTC."""
     now = now or datetime.now(timezone.utc)
     address, tz, show_utc = (to, "UTC", False) if isinstance(to, str) else \
         (to.address, getattr(to.tz, "key", None) or "UTC", to.show_utc)
     row = EmailOutbox(kind=kind, recipient=address, tz=tz, show_utc=show_utc,
                       subject=subject, text=text, html=html, retry=retry, created_at=now,
-                      state="held" if send_after else "pending", send_after=send_after,
-                      next_attempt_at=send_after or now)
+                      state="held" if send_after else "sending" if claimed else "pending",
+                      send_after=send_after, next_attempt_at=send_after or now,
+                      claimed_at=now if claimed else None)
     db.add(row)
     return row
 
@@ -219,14 +223,18 @@ async def write_held(app: "Quart", db, row: EmailOutbox) -> None:
     row.subject, row.text, row.html = alert_words(app.config.get("SMTP", {}), alerts, to)
 
 
-async def attempt(app: "Quart", ids: list[str], now: datetime | None = None) -> dict[str, str]:
+async def attempt(app: "Quart", ids: list[str], now: datetime | None = None,
+                  cfg: dict | None = None) -> dict[str, EmailOutbox]:
     """Try to send the claimed rows `ids` once, and settle each. The words
     are written and kept first, so a retry sends the same email; no session
-    is held while the mail server is talked to. Returns {id: state after}."""
+    is held while the mail server is talked to. `cfg` replaces the saved mail
+    settings for this one try (a test of the form's unsaved values; such a
+    row has retry=False, so nothing later needs them). Returns {id: row}
+    as settled."""
     from steward.core.mail import message
     if not ids:
         return {}
-    cfg = app.config.get("SMTP", {})
+    cfg = cfg if cfg is not None else app.config.get("SMTP", {})
     outcomes: dict[str, BaseException | None] = {}
     sendable: list[tuple[str, EmailMessage]] = []
     async with app.db_sessionmaker() as db:
@@ -257,7 +265,7 @@ async def attempt(app: "Quart", ids: list[str], now: datetime | None = None) ->
                 if row.state == "failed":
                     logger.warning("email %s to %s failed: %s", row.kind, row.recipient, row.last_error)
             await after_settle(db, rows)
-        return {row.id: row.state for row in rows}
+        return {row.id: row for row in rows}
 
 
 async def after_settle(db, rows: list[EmailOutbox]) -> None:
@@ -315,6 +323,36 @@ async def send_due(app: "Quart") -> None:
     now = datetime.now(timezone.utc)
     ids = await claim_due(app, now)
     if ids:
-        states = await attempt(app, ids, now)
-        logger.info("email outbox: %d tried, %d sent", len(states),
-                    sum(1 for s in states.values() if s == "sent"))
+        rows = await attempt(app, ids, now)
+        logger.info("email outbox: %d tried, %d sent", len(rows),
+                    sum(1 for r in rows.values() if r.state == "sent"))
+
+
+async def send_each(app: "Quart", kind: str, to: list, words: Callable[..., tuple],
+                    *, retry: bool = True, cfg: dict | None = None) -> list[EmailOutbox]:
+    """Queue one email per reader in `to` (mail.Recipient or address),
+    written by `words(reader)` -> (subject, text, html), and try them at
+    once, for a page that answers with what happened (see `said`). Returns
+    the rows as settled: a temporary failure is left pending for the sender
+    to retry, unless retry=False (a test). `cfg` as for `attempt`."""
+    async with app.db_sessionmaker() as db:
+        async with db.begin():
+            rows = [enqueue(db, kind=kind, to=r, subject=s, text=t, html=h, retry=retry, claimed=True)
+                    for r in to for s, t, h in [words(r)]]
+            await db.flush()
+            ids = [r.id for r in rows]
+    done = await attempt(app, ids, cfg=cfg)
+    return [done[i] for i in ids if i in done]
+
+
+def said(rows: list[EmailOutbox]) -> tuple[bool, str]:
+    """(all sent, what happened) for rows just tried: who it went to, who
+    refused and why, and who Steward is still trying."""
+    sent = [r.recipient for r in rows if r.state == "sent"]
+    failed = [f"{r.recipient}: {r.last_error}" for r in rows if r.state == "failed"]
+    later = [f"{r.recipient} ({r.last_error})" for r in rows if r.state == "pending"]
+    parts = ([f"Sent to {', '.join(sent)}."] if sent else []) + \
+        ([f"Not sent to {'; '.join(failed)}."] if failed else []) + \
+        ([f"Not sent yet to {'; '.join(later)}; Steward will try again for up to an hour."]
+         if later else [])
+    return bool(rows) and not failed and not later, " ".join(parts)
diff --git a/steward/core/reports.py b/steward/core/reports.py
index f3a88f4..21634fb 100644
--- a/steward/core/reports.py
+++ b/steward/core/reports.py
@@ -11,7 +11,7 @@ from sqlalchemy import and_, case, func, select
 
 from steward.alerts import service as alert_svc
 from steward.core.formatting import zone
-from steward.core.mail import message, recipients, report_email, send
+from steward.core.mail import recipients, report_email
 from steward.core.settings import get_setting
 from steward.models.alerts import AlertEvent
 from steward.models.metrics import PluginMetric
@@ -134,13 +134,13 @@ async def send_report(app) -> tuple[bool, str]:
         logger.exception("Failed to build report data")
         return False, f"Data collection failed: {exc}"
 
-    try:
-        await send(smtp_cfg, [message(smtp_cfg, r.address, *report_email(smtp_cfg, data, r)) for r in to])
-    except Exception as exc:
-        logger.error("Failed to send weekly report: %s", exc)
-        return False, f"Send failed: {exc}"
-    logger.info("Weekly report sent to %d address(es)", len(to))
-    return True, f"Report sent to {', '.join(r.address for r in to)}."
+    from steward.core import outbox
+    # Queued, then tried at once so the button can say what happened; one
+    # the server didn't take yet stays queued and is retried for an hour.
+    ok, said = outbox.said(await outbox.send_each(
+        app, "report", to, lambda r: report_email(smtp_cfg, data, r)))
+    logger.info("Weekly report: %s", said)
+    return ok, said
 
 
 def report_due(now: datetime, day: int, hour: int, tz) -> bool:
diff --git a/steward/settings/routes.py b/steward/settings/routes.py
index 19c2b33..3247dce 100644
--- a/steward/settings/routes.py
+++ b/steward/settings/routes.py
@@ -319,7 +319,8 @@ async def test_email():
     the zone chosen for them. A blank password uses the saved one."""
     from steward.core.formatting import zone
     from steward.core.mail import Recipient, alert_email, is_real_address, pick_recipients
-    from steward.core.notifications import _send_email, smtp_mode
+    from steward.core import outbox
+    from steward.core.notifications import smtp_mode
     from steward.models.users import User
     form = await request.form
     async with current_app.db_sessionmaker() as db:
@@ -345,11 +346,12 @@ async def test_email():
             "email", False, "Your account has no email address mail can reach, and no Also send to "
                             "addresses are entered. Set your address on the Account page.")
     alert = _sample_alert()
-    sent = await _send_email(cfg, alert, to)
+    # Queued and recorded like any email, tried once with the form's values.
+    ok, said = outbox.said(await outbox.send_each(
+        current_app, "test", to, lambda r: alert_email(cfg, alert, r), retry=False, cfg=cfg))
     how = {"ssl": "implicit TLS", "starttls": "STARTTLS", "plain": "no TLS"}[smtp_mode(port, cfg["tls"])]
-    result = (f"Sent to {', '.join(r.address for r in to)} via {cfg['host']}:{port} ({how})."
-              if sent["sent"] else f"{cfg['host']}:{port} ({how}): {sent['error']}")
-    return await _notify_test_result("email", sent["sent"], result, alert_email(cfg, alert, to[0])[1])
+    result = f"{said[:-1]} via {cfg['host']}:{port} ({how})." if ok else f"{cfg['host']}:{port} ({how}): {said}"
+    return await _notify_test_result("email", ok, result, alert_email(cfg, alert, to[0])[1])
 
 
 # ── Ansible Sources ───────────────────────────────────────────────────────────
diff --git a/steward/settings/users.py b/steward/settings/users.py
index d674475..e536b15 100644
--- a/steward/settings/users.py
+++ b/steward/settings/users.py
@@ -185,12 +185,15 @@ async def _deliver(invite: UserInvite, key: str) -> str | None:
     url = invites.link(public_base_url(request), key)
     subject, text, html = mail.invite_email(session.get("username", "An admin"), invite.role.value,
                                             invite.expires_at, url, zone(session.get("tz")))
-    try:
-        await mail.send(cfg, [mail.message(cfg, invite.email, subject, text, html)])
-    except Exception as exc:
-        current_app.logger.warning("Invite email to %s failed: %s", invite.email, exc)
-        return f"Sending to {invite.email} failed ({exc})."
-    return None
+    from steward.core import outbox
+    (row,) = await outbox.send_each(current_app, "invite", [invite.email],
+                                    lambda _: (subject, text, html))
+    if row.state == "sent":
+        return None
+    if row.state == "pending":
+        return (f"Sending to {invite.email} didn't go through yet ({row.last_error}); "
+                f"Steward will keep trying for up to an hour.")
+    return f"Sending to {invite.email} failed ({row.last_error})."
 
 
 async def _link_page(invite: UserInvite, key: str, why: str):
diff --git a/tests/core/test_mail.py b/tests/core/test_mail.py
index 7c0648a..e3a9014 100644
--- a/tests/core/test_mail.py
+++ b/tests/core/test_mail.py
@@ -6,7 +6,6 @@ from datetime import datetime, timezone
 from zoneinfo import ZoneInfo
 
 from steward.core import mail
-from steward.core import notifications as n
 from steward.core import reports
 
 ALERT = {"rule_name": 'Disk <b>"root"</b> on web01', "state": "FIRING", "metric": "disk_used_pct",
@@ -46,9 +45,8 @@ def test_every_colour_is_a_theme_value():
 
 
 async def _sent(monkeypatch, cfg, alert, to=(EXTRA_NY,)):
-    out = []
-    monkeypatch.setattr(n, "_smtp_send_sync", lambda c, msgs: out.extend(msgs))
-    assert (await n._send_email(cfg, alert, list(to)))["sent"]
+    """The message each of `to` is handed for `alert`, as the outbox writes it."""
+    out = [mail.message(cfg, r.address, *mail.alert_email(cfg, alert, r)) for r in to]
     return out[0] if len(to) == 1 else out
 
 
@@ -140,12 +138,21 @@ async def test_the_report_is_sent_from_the_configured_address(monkeypatch):
         assert kind == "report"
         return [PERSON_NY, EXTRA_NY]
 
+    from types import SimpleNamespace
+    from steward.core import outbox
     out = []
+
+    async def _send_each(app, kind, to, words, **kw):
+        # Queued then tried at once (#5508); here every one is accepted.
+        assert kind == "report" and kw.get("retry", True)
+        out.extend(mail.message(app.config["SMTP"], r.address, *words(r)) for r in to)
+        return [SimpleNamespace(recipient=r.address, state="sent", last_error=None) for r in to]
+
     monkeypatch.setattr(reports, "build_report_data", _data)
     monkeypatch.setattr(reports, "recipients", _recipients)
-    monkeypatch.setattr(n, "_smtp_send_sync", lambda c, msgs: out.extend(msgs))
+    monkeypatch.setattr(outbox, "send_each", _send_each)
     ok, said = await reports.send_report(_App())
-    assert ok and said == "Report sent to ann@example.com, ops@example.com."
+    assert ok and said == "Sent to ann@example.com, ops@example.com."
     assert [(m["From"], m["To"]) for m in out] == [("alerts@example.com", "ann@example.com"),
                                                    ("alerts@example.com", "ops@example.com")]
     assert all(m.get_content_type() == "multipart/alternative" for m in out)
diff --git a/tests/core/test_notifications.py b/tests/core/test_notifications.py
index f969165..2d388bd 100644
--- a/tests/core/test_notifications.py
+++ b/tests/core/test_notifications.py
@@ -49,7 +49,7 @@ def test_a_bad_template_raises_valueerror_saying_why(tpl, says):
         n.render_webhook(tpl, ALERT)
 
 
-# ── smtp_mode / _smtp_send_sync ───────────────────────────────────────────────
+# ── smtp_mode / smtp_open (via outbox.deliver_sync) ───────────────────────────────────────────────
 
 @pytest.mark.parametrize("port, tls, mode", [
     (465, True, "ssl"), (465, False, "ssl"), ("465", False, "ssl"),
@@ -98,27 +98,30 @@ class SMTP_SSL(_FakeSMTP):
     (25, False, [("connect", "SMTP", "mx", 25, n.SMTP_TIMEOUT_S)]),
 ])
 def test_smtp_send_connects_by_mode_with_a_timeout(monkeypatch, port, tls, expected):
+    from email.message import EmailMessage
+    from steward.core import outbox
     monkeypatch.setattr(n.smtplib, "SMTP", SMTP)
     monkeypatch.setattr(n.smtplib, "SMTP_SSL", SMTP_SSL)
     _FakeSMTP.made = []
-    msgs = [n.EmailMessage(), n.EmailMessage()]
+    msgs = [EmailMessage(), EmailMessage()]
     msgs[0]["From"], msgs[1]["From"] = "steward@example.com", "other@example.com"
-    n._smtp_send_sync({"host": "mx", "port": port, "tls": tls, "username": "u", "password": "p"}, msgs)
+    cfg = {"host": "mx", "port": port, "tls": tls, "username": "u", "password": "p"}
+    assert outbox.deliver_sync(cfg, msgs) == [None, None]
     (smtp,) = _FakeSMTP.made  # every message over one connection
     assert smtp.calls == expected + [("login", "u", "p"), ("send", "steward@example.com"),
                                      ("send", "other@example.com")]
 
 
-async def test_email_from_falls_back_and_a_line_break_in_the_name_still_sends(monkeypatch):
+def test_email_from_falls_back_and_a_line_break_in_the_name_still_sends():
+    from steward.core.mail import alert_email, message
     sent = []
-    monkeypatch.setattr(n, "_smtp_send_sync",
-                        lambda cfg, msgs: sent.extend((m["From"], m["Subject"]) for m in msgs))
-    to = [Recipient("a@example.com", timezone.utc, False)]
+    to = Recipient("a@example.com", timezone.utc, False)
     base = {"host": "mx", "port": 587}
     for cfg in ({**base, "from": "alerts@example.com", "username": "u@example.com"},
                 {**base, "from": "", "username": "u@example.com"},
                 {**base, "from": "", "username": ""}):
-        assert (await n._send_email(cfg, ALERT, to))["sent"]
+        m = message(cfg, to.address, *alert_email(cfg, ALERT, to))
+        sent.append((m["From"], m["Subject"]))
     assert [f for f, _ in sent] == ["alerts@example.com", "u@example.com", "steward@localhost"]
     # The rule name has a line break; the subject folds it to a space rather than failing.
     assert sent[0][1] == '[Steward] Firing: Disk "root" on web01 \\ backslash — web01 94%'
diff --git a/tests/core/test_outbox.py b/tests/core/test_outbox.py
index 792ac77..b1a0cfd 100644
--- a/tests/core/test_outbox.py
+++ b/tests/core/test_outbox.py
@@ -186,3 +186,40 @@ def test_several_alerts_are_one_email_listing_each_oldest_first():
         assert f"Agent offline: {host}" in text and f"Agent offline: {host}" in html
     assert text.index("web01") < text.index("web02") < text.index("db01")
     assert "Fri 9 Oct 2026 08:00 EDT" in text                                # the reader's zone
+
+
+def test_said_names_who_got_it_who_refused_and_who_is_still_being_tried():
+    rows = [_row(recipient="a@x", state="sent"),
+            _row(recipient="b@x", state="failed", last_error="550 no such user"),
+            _row(recipient="c@x", state="pending", last_error="451 greylisted")]
+    ok, said = outbox.said(rows)
+    assert not ok
+    assert said == ("Sent to a@x. Not sent to b@x: 550 no such user. Not sent yet to c@x "
+                    "(451 greylisted); Steward will try again for up to an hour.")
+    assert outbox.said(rows[:1]) == (True, "Sent to a@x.")
+    assert outbox.said([])[0] is False
+
+
+# The guard: every email goes through the queue (System 156 ruling), so the
+# only code that opens a connection to the mail server is the outbox's.
+def _smtp_openers(sources: dict[str, str]) -> set[str]:
+    import re
+    opens = re.compile(r"\bsmtp_open\(|\bsmtplib\.SMTP(_SSL)?\(")
+    return {path for path, src in sources.items()
+            if any(opens.search(line) and not line.lstrip().startswith(("#", "def "))
+                   for line in src.splitlines())}
+
+
+def test_only_the_outbox_talks_to_the_mail_server():
+    from pathlib import Path
+    root = Path(__file__).resolve().parents[2]          # the checkout
+    sources = {str(p.relative_to(root)): p.read_text() for p in (root / "steward").rglob("*.py")}
+    sources.update({str(p.relative_to(root)): p.read_text() for p in (root / "plugins").rglob("*.py")}
+                   if (root / "plugins").is_dir() else {})
+    assert _smtp_openers(sources) == {"steward/core/outbox.py", "steward/core/notifications.py"}
+
+
+def test_the_smtp_guard_can_fail():
+    assert _smtp_openers({"x.py": "    with smtplib.SMTP(host) as s:"}) == {"x.py"}
+    assert _smtp_openers({"y.py": "    smtp = notifications.smtp_open(cfg)"}) == {"y.py"}
+    assert _smtp_openers({"z.py": "# smtp_open(cfg) is the outbox's\ndef smtp_open(cfg):"}) == set()
diff --git a/tests/integration/_mail.py b/tests/integration/_mail.py
new file mode 100644
index 0000000..2ebb867
--- /dev/null
+++ b/tests/integration/_mail.py
@@ -0,0 +1,29 @@
+"""Email in integration tests: every email is a queued row the outbox sends
+(#5506), so a test catches what the mail server would have been handed by
+replacing the one SMTP conversation, outbox.deliver_sync."""
+from __future__ import annotations
+
+from email.message import EmailMessage
+
+
+def capture(app, monkeypatch, answer=None) -> list[EmailMessage]:
+    """Set a mail server and collect every message the outbox delivers.
+    `answer(msg)` is the server's reply to each (None: accepted)."""
+    from steward.core import outbox
+    sent: list[EmailMessage] = []
+
+    def deliver(cfg, messages):
+        sent.extend(messages)
+        return [answer(m) if answer else None for m in messages]
+
+    app.config["SMTP"] = {**app.config.get("SMTP", {}), "host": "mx.example", "port": 587,
+                          "from": "steward@example.com"}
+    monkeypatch.setattr(outbox, "deliver_sync", deliver)
+    return sent
+
+
+def to(sent: list[EmailMessage], *addresses: str) -> list[EmailMessage]:
+    """The messages among `sent` addressed to any of `addresses` (other
+    tests' queued email can go out in the same tick)."""
+    want = {a.lower() for a in addresses}
+    return [m for m in sent if m["To"].lower() in want]
diff --git a/tests/integration/test_alert_email_outbox.py b/tests/integration/test_alert_email_outbox.py
index 17a0e2d..d092d14 100644
--- a/tests/integration/test_alert_email_outbox.py
+++ b/tests/integration/test_alert_email_outbox.py
@@ -81,7 +81,7 @@ def test_alerts_in_one_window_are_one_email_and_each_event_records_it(app, monke
     from steward.core import outbox
 
     tag = uuid.uuid4().hex[:8]
-    extra = f"oncall-{tag}@test"
+    extra = f"oncall-{tag}@example.com"
     app.config["SMTP"] = {"host": "mx.test", "port": 587, "from": "steward@test",
                           "recipients": [extra], "tz": "America/New_York"}
     t0 = datetime(2026, 10, 9, 12, 0, tzinfo=timezone.utc)
@@ -142,7 +142,7 @@ def test_an_email_whose_alerts_were_deleted_fails_and_says_so(app, monkeypatch):
     from steward.models.alerts import AlertEvent
 
     tag = uuid.uuid4().hex[:8]
-    extra = f"gone-{tag}@test"
+    extra = f"gone-{tag}@example.com"
     app.config["SMTP"] = {"host": "mx.test", "port": 587, "from": "steward@test", "recipients": [extra]}
     monkeypatch.setattr(outbox, "deliver_sync", lambda cfg, msgs: [None] * len(msgs))
     t0 = datetime.now(timezone.utc)
@@ -155,8 +155,8 @@ def test_an_email_whose_alerts_were_deleted_fails_and_says_so(app, monkeypatch):
         async with app.db_sessionmaker() as s:
             async with s.begin():
                 await s.execute(delete(AlertEvent).where(AlertEvent.id == ev))
-        states = await outbox.attempt(app, [row.id])
-        return states[row.id], row.id
+        done = await outbox.attempt(app, [row.id])
+        return done[row.id].state, row.id
 
     state, rid = asyncio.run(_go())
     assert state == "failed"
diff --git a/tests/integration/test_alert_send_test.py b/tests/integration/test_alert_send_test.py
index b5d812d..f62e1d5 100644
--- a/tests/integration/test_alert_send_test.py
+++ b/tests/integration/test_alert_send_test.py
@@ -39,11 +39,8 @@ def test_send_test_reaches_each_channel_and_leaves_the_rule_alone(app, monkeypat
     from steward.models.audit import AuditEvent
     from steward.models.users import User, UserRole
 
-    emails, hooks = [], []
-
-    async def fake_email(cfg, alert, to):
-        emails.append((alert, [r.address for r in to]))
-        return {"sent": True, "error": None}
+    from tests.integration._mail import capture
+    hooks = []
 
     async def fake_hook(cfg, alert):
         hooks.append(alert)
@@ -52,10 +49,9 @@ def test_send_test_reaches_each_channel_and_leaves_the_rule_alone(app, monkeypat
     async def fake_recipients(db, kind, smtp):
         return [mail.Recipient("ann@example.com", ZoneInfo("UTC"), False, "ann")]
 
-    monkeypatch.setattr(notifications, "_send_email", fake_email)
+    emails = capture(app, monkeypatch)
     monkeypatch.setattr(notifications, "_send_webhook", fake_hook)
     monkeypatch.setattr(mail, "recipients", fake_recipients)
-    app.config["SMTP"] = {"host": "mx.example", "port": 587, "from": "alerts@example.com"}
     app.config["WEBHOOK"] = {"url": "https://hook.example/api/1"}
 
     async def _go():
@@ -83,12 +79,20 @@ def test_send_test_reaches_each_channel_and_leaves_the_rule_alone(app, monkeypat
         assert resp.status_code == 200
         page = await resp.get_data(as_text=True)
         assert "alert-error" in page
-        assert "Email sent to ann@example.com." in page
+        assert "Email: Sent to ann@example.com." in page
         assert "Webhook to hook.example failed: connection refused" in page
 
-        # What went out is this rule, marked TEST, at its latest reading.
-        ((alert, to),) = emails
-        assert to == ["ann@example.com"] and hooks == [alert]
+        # What went out is this rule, marked TEST, at its latest reading: one
+        # queued test email (recorded, not retried) and the webhook.
+        (msg,) = emails
+        (alert,) = hooks
+        assert msg["To"] == "ann@example.com" and f"Hot {tag}" in msg["Subject"]
+        from steward.models.outbox import EmailOutbox
+        async with app.db_sessionmaker() as s:
+            row = (await s.execute(select(EmailOutbox).where(
+                EmailOutbox.recipient == "ann@example.com", EmailOutbox.kind == "test",
+                EmailOutbox.subject == msg["Subject"]))).scalars().one()
+        assert (row.state, row.retry, row.attempts) == ("sent", False, 1)
         assert (alert["rule_name"], alert["state"], alert["resource"], alert["value"]) == (
             f"Hot {tag}", "TEST", host, 42.0)
 
diff --git a/tests/integration/test_invites.py b/tests/integration/test_invites.py
index 3179225..11d908b 100644
--- a/tests/integration/test_invites.py
+++ b/tests/integration/test_invites.py
@@ -62,16 +62,9 @@ async def _audits(app, uid):
     return [(r.action, json.loads(r.detail_json or "{}")) for r in rows]
 
 
-def _mail(app, monkeypatch):
-    from steward.core import mail
-    sent = []
-
-    async def fake_send(cfg, messages):
-        sent.extend(messages)
-
-    app.config["SMTP"] = {"host": "mx.example", "port": 587, "from": "steward@example.com"}
-    monkeypatch.setattr(mail, "send", fake_send)
-    return sent
+def _mail(app, monkeypatch, answer=None):
+    from tests.integration._mail import capture
+    return capture(app, monkeypatch, answer)
 
 
 def test_an_invite_is_emailed_and_the_invitee_makes_their_own_account_once(app, monkeypatch):
@@ -193,3 +186,27 @@ def test_an_address_with_an_account_is_not_invited_and_only_an_admin_invites(app
                                     form={"email": "y@example.com"})).status_code == 403
 
     asyncio.run(_go())
+
+
+def test_an_invite_the_server_refuses_or_defers_shows_the_link_and_why(app, monkeypatch):
+    # Sent through the queue (#5508) and tried at once: a refusal says so; a
+    # "try later" says Steward keeps trying; either way the link is shown.
+    import smtplib
+    answers = {}
+    _mail(app, monkeypatch, lambda m: answers.get(m["To"]))
+
+    async def _go():
+        admin, aid, _ = await _admin(app)
+        refused, later = f"no-{aid[:8]}@example.com", f"later-{aid[:8]}@example.com"
+        answers[refused] = smtplib.SMTPRecipientsRefused({refused: (550, b"no such user")})
+        answers[later] = smtplib.SMTPDataError(451, b"greylisted")
+        resp = await admin.post("/settings/users/invite", headers=CSRF,
+                                form={"email": refused, "role": "viewer", "days": "7"})
+        page = await resp.get_data(as_text=True)
+        assert f"Sending to {refused} failed (550 no such user)." in page and "/invite/" in page
+        resp = await admin.post("/settings/users/invite", headers=CSRF,
+                                form={"email": later, "role": "viewer", "days": "7"})
+        page = await resp.get_data(as_text=True)
+        assert "451 greylisted" in page and "keep trying for up to an hour" in page
+
+    asyncio.run(_go())
diff --git a/tests/integration/test_notification_test_send.py b/tests/integration/test_notification_test_send.py
index e030b96..427d3fb 100644
--- a/tests/integration/test_notification_test_send.py
+++ b/tests/integration/test_notification_test_send.py
@@ -90,14 +90,14 @@ def test_test_webhook_sends_the_form_template_and_shows_the_body(app, monkeypatc
 
 
 def test_test_email_uses_the_form_settings_and_names_the_tls_mode(app, monkeypatch):
-    from steward.core import notifications
+    from steward.core import outbox
     sent = []
 
-    async def fake_send(cfg, alert, to):
-        sent.append((cfg, [r.address for r in to]))
-        return {"sent": True, "error": None}
+    def fake_deliver(cfg, messages):
+        sent.append((cfg, [m["To"] for m in messages]))
+        return [None] * len(messages)
 
-    monkeypatch.setattr(notifications, "_send_email", fake_send)
+    monkeypatch.setattr(outbox, "deliver_sync", fake_deliver)
 
     async def _go():
         client, uid = await _admin_client(app)
@@ -110,10 +110,18 @@ def test_test_email_uses_the_form_settings_and_names_the_tls_mode(app, monkeypat
         assert "alert-success" in page
         assert "Sent to a@example.com, b@example.com via mx.example:465 (implicit TLS)." in page
         assert "Rule: Test alert" in page
-        # The admin's own address (uuid@test) isn't one mail can reach, so only the typed ones.
+        # The admin's own address (uuid@test) isn't one mail can reach, so only the typed ones,
+        # sent through the queue with the form's unsaved values, recorded, and not retried.
         assert sent == [({"host": "mx.example", "port": 465, "tls": False, "username": "u",
                           "password": "pw", "from": "alerts@example.com", "base_url": ""},
                          ["a@example.com", "b@example.com"])]
+        from sqlalchemy import select
+        from steward.models.outbox import EmailOutbox
+        async with app.db_sessionmaker() as s:
+            rows = (await s.execute(select(EmailOutbox).where(
+                EmailOutbox.kind == "test", EmailOutbox.recipient.in_(["a@example.com", "b@example.com"]))
+                .order_by(EmailOutbox.created_at.desc()).limit(2))).scalars().all()
+        assert {(r.state, r.retry) for r in rows} == {("sent", False)}
 
         resp = await client.post("/settings/notifications/test-email", form={
             "smtp.host": "", "smtp.port": "587", "smtp.recipients": ""}, headers=csrf)
diff --git a/tests/integration/test_passwords.py b/tests/integration/test_passwords.py
index d85cfcd..477c47a 100644
--- a/tests/integration/test_passwords.py
+++ b/tests/integration/test_passwords.py
@@ -123,15 +123,14 @@ _KEY = re.compile(r"/reset/([A-Za-z0-9_-]{20,})")
 
 
 def _mail(app, monkeypatch):
-    from steward.core import mail
-    sent = []
+    from tests.integration._mail import capture
+    return capture(app, monkeypatch)
 
-    async def fake_send(cfg, messages):
-        sent.extend(messages)
 
-    app.config["SMTP"] = {"host": "mx.example", "port": 587, "from": "steward@example.com"}
-    monkeypatch.setattr(mail, "send", fake_send)
-    return sent
+async def _deliver(app):
+    """The outbox sender's next tick: a reset email is queued (#5508)."""
+    from steward.core import outbox
+    await outbox.send_due(app)
 
 
 async def _stranger(app):
@@ -158,8 +157,11 @@ def test_a_forgotten_password_is_reset_from_the_emailed_link(app, monkeypatch):
             resp = await guest.post("/forgot", headers=CSRF, form={"name": who})
             answers.append((resp.status_code, "on its way" in await resp.get_data(as_text=True)))
         assert answers == [(200, True)] * 3
-        assert [m["To"] for m in sent] == [f"{name}@example.com"]
-        text = sent[0].get_body(("plain",)).get_content()
+        await _deliver(app)
+        from tests.integration._mail import to
+        mine = to(sent, f"{name}@example.com", f"{sso_name}@example.com", f"nobody-{uid[:8]}@example.com")
+        assert [m["To"] for m in mine] == [f"{name}@example.com"]
+        text = mine[0].get_body(("plain",)).get_content()
         assert name in text and "BST" in text
         key = _KEY.search(text).group(1)
 
@@ -197,7 +199,10 @@ def test_asking_again_kills_the_first_link_and_an_old_link_expires(app, monkeypa
         guest = await _stranger(app)
         for _ in range(2):
             await guest.post("/forgot", headers=CSRF, form={"name": name})
-        first, second = (_KEY.search(m.get_body(("plain",)).get_content()).group(1) for m in sent)
+        await _deliver(app)
+        from tests.integration._mail import to
+        first, second = (_KEY.search(m.get_body(("plain",)).get_content()).group(1)
+                         for m in to(sent, f"{name}@example.com"))
         assert (await guest.get(f"/reset/{first}")).status_code == 404
         assert (await guest.get(f"/reset/{second}")).status_code == 200