diff --git a/tests/integration/test_host_metrics.py b/tests/integration/test_host_metrics.py
index be561aa..ee09572 100644
--- a/tests/integration/test_host_metrics.py
+++ b/tests/integration/test_host_metrics.py
@@ -120,8 +120,11 @@ def test_rollup_aggregates_old_raw_and_prunes(app):
             return counts, hrly, raw_left
 
     counts, hrly, raw_left = asyncio.run(_go())
-    assert counts["buckets_rolled"] == 1
-    assert counts["raw_rows_rolled"] == 2
+    # The counts span the whole table, which other tests share (docker
+    # snapshots are recorded at their own, older times, #5752): this host's
+    # bucket is checked exactly below.
+    assert counts["buckets_rolled"] >= 1
+    assert counts["raw_rows_rolled"] >= 2
     assert len(hrly) == 1
     assert abs(float(hrly[0][0]) - 15.0) < 0.001   # avg(10, 20)
     assert hrly[0][1] == 2