diff --git a/nextcloud_mcp_server/vector/processor.py b/nextcloud_mcp_server/vector/processor.py
index 190f207f..05619b18 100644
--- a/nextcloud_mcp_server/vector/processor.py
+++ b/nextcloud_mcp_server/vector/processor.py
@@ -507,10 +507,11 @@ async def process_document(
     one outer attempt (~30s) and defers. Don't stack a third retry layer here.
     """
     # EscalateError is a control-flow signal that arises ONLY on the per-tier
-    # external path (tier set). Bind the class lazily there so the in-process /
-    # memory path never pulls the document stack at call time (mirrors the lazy
-    # get_registry import; see #877). When tier is None it can't be raised, so
-    # the guards below stay inert.
+    # external path (tier set). Bind the class lazily here, and only when a tier
+    # is set, so the document stack is never imported at *module load* (the #877
+    # invariant) nor on the delete / text-doc call paths (file processing already
+    # imports it via get_registry regardless). When tier is None it can't be
+    # raised, so the guards below stay inert.
     escalate_error_cls: type[BaseException] | None = None
     if tier is not None:
         from nextcloud_mcp_server.document_processors.escalation import (  # noqa: PLC0415
diff --git a/tests/unit/test_ingest_queue_depth_metric.py b/tests/unit/test_ingest_queue_depth_metric.py
index 9ff5a5d5..0fb1a169 100644
--- a/tests/unit/test_ingest_queue_depth_metric.py
+++ b/tests/unit/test_ingest_queue_depth_metric.py
@@ -5,6 +5,7 @@ procrastinate's ``list_queues_async``) must read 0, not its last non-zero value.
 """
 
 import pytest
+from pytest import approx
 
 from nextcloud_mcp_server.observability.metrics import update_ingest_queue_depth
 
@@ -14,19 +15,27 @@ _METRIC = "astrolabe_ingest_queue_depth"
 
 
 def test_drained_queue_zeroes_not_stale(metric_sample):
-    # ocr has a backlog this tick.
+    # ocr has a backlog this tick. (pytest.approx: the gauge sample is a float.)
     update_ingest_queue_depth({"ingest-ocr": {"todo": 4}})
-    assert metric_sample(_METRIC, {"queue": "ingest-ocr", "status": "todo"}) == 4.0
+    assert metric_sample(_METRIC, {"queue": "ingest-ocr", "status": "todo"}) == approx(
+        4
+    )
 
     # Next tick ocr has drained → procrastinate omits it from by_queue entirely.
     update_ingest_queue_depth({"ingest-fast": {"todo": 1}})
     # The gauge must read 0 for the drained queue, not the stale 4.
-    assert metric_sample(_METRIC, {"queue": "ingest-ocr", "status": "todo"}) == 0.0
-    assert metric_sample(_METRIC, {"queue": "ingest-fast", "status": "todo"}) == 1.0
+    assert metric_sample(_METRIC, {"queue": "ingest-ocr", "status": "todo"}) == approx(
+        0
+    )
+    assert metric_sample(_METRIC, {"queue": "ingest-fast", "status": "todo"}) == approx(
+        1
+    )
 
 
 def test_none_is_noop(metric_sample):
     update_ingest_queue_depth({"ingest-fast": {"doing": 2}})
     # Memory backend passes None → must not wipe the last published values.
     update_ingest_queue_depth(None)
-    assert metric_sample(_METRIC, {"queue": "ingest-fast", "status": "doing"}) == 2.0
+    assert metric_sample(
+        _METRIC, {"queue": "ingest-fast", "status": "doing"}
+    ) == approx(2)
diff --git a/tests/unit/vector/test_tiered_escalation_strategy.py b/tests/unit/vector/test_tiered_escalation_strategy.py
index bbb08eff..aa976efb 100644
--- a/tests/unit/vector/test_tiered_escalation_strategy.py
+++ b/tests/unit/vector/test_tiered_escalation_strategy.py
@@ -91,16 +91,22 @@ class TestTieredEscalationStrategy:
 
     def test_transient_backoff_progression(self):
         # min(4 * 2**(attempts-1), 300): 4, 8, 16, ... capped at 300s.
+        # procrastinate sets retry_at = utcnow() + wait at call time. Bracketing
+        # the call with before/after makes the assertion exact and independent of
+        # runner load: with before <= call_now <= after, we have
+        #   (retry_at - after) <= wait <= (retry_at - before).
         strat = self._strategy(max_transient=100)
         for attempts, expected in [(1, 4), (2, 8), (3, 16), (4, 32), (20, 300)]:
+            before = datetime.now(timezone.utc)
             decision = strat.get_retry_decision(
                 exception=httpx.ConnectError("x"), job=_job(attempts=attempts)
             )
+            after = datetime.now(timezone.utc)
             assert decision is not None and decision.retry_at is not None
-            delta = (decision.retry_at - datetime.now(timezone.utc)).total_seconds()
-            # retry_at = now + wait; allow a small window for execution time.
-            assert expected - 2 <= delta <= expected + 1, (
-                f"attempts={attempts}: delta={delta:.2f}s, expected≈{expected}s"
+            lo = (decision.retry_at - after).total_seconds()
+            hi = (decision.retry_at - before).total_seconds()
+            assert lo <= expected <= hi, (
+                f"attempts={attempts}: expected={expected}s not in [{lo:.3f}, {hi:.3f}]"
             )
 
     def test_transient_gives_up_over_cap(self):