diff --git a/src/openultrasast/model/scan.py b/src/openultrasast/model/scan.py
index 9a0f7bd..4da8bcf 100644
--- a/src/openultrasast/model/scan.py
+++ b/src/openultrasast/model/scan.py
@@ -922,6 +922,8 @@ def _batched(
 # a mis-estimate is bounded and a kill costs little.
 PORTION_TARGET_SECONDS = 120.0
 PORTION_FIXED_SECONDS = 70.0  # measured start-and-load on a 4 MB graph
+PORTION_MIN_INFORMATIVE_SECONDS = 10.0  # less work than this above the fixed start says nothing about cost per visit
+PORTION_MAX_GROWTH = 2.0  # a budget may double per portion, never more
 
 
 class _PortionSizer:
@@ -965,9 +967,15 @@ class _PortionSizer:
             self.budget = max(1.0, self.budget / 2)
             logger.info("cpg portion of %d sink visit(s) did not answer in %.0fs; budget halved to %d", visits, seconds, int(self.budget))
             return
-        per_visit = max(0.0, seconds - PORTION_FIXED_SECONDS) / visits
-        if per_visit > 0:
-            self.budget = max(1.0, (PORTION_TARGET_SECONDS - PORTION_FIXED_SECONDS) / per_visit)
+        work = seconds - PORTION_FIXED_SECONDS
+        # A portion that finished inside the fixed start carries no information about cost per visit -- 3 s
+        # of work over 199 visits read as 0.015 s each and the next budget grew thirteen-fold to 3,404, which
+        # the ceiling then killed. Measured on the plugin. So a sample below the floor is not extrapolated
+        # from, and growth is capped at doubling per step: the sizing may be wrong, but never by more than
+        # one factor of two per portion, which a kill can then undo.
+        if work >= PORTION_MIN_INFORMATIVE_SECONDS:
+            fitted = (PORTION_TARGET_SECONDS - PORTION_FIXED_SECONDS) / (work / visits)
+            self.budget = max(1.0, min(fitted, self.budget * PORTION_MAX_GROWTH))
         logger.info("cpg portion of %d sink visit(s) answered in %.0fs; next budget %d visit(s)", visits, seconds, int(self.budget))
 
 
diff --git a/tests/test_model_scope.py b/tests/test_model_scope.py
index bb3d48a..3f20903 100644
--- a/tests/test_model_scope.py
+++ b/tests/test_model_scope.py
@@ -338,3 +338,10 @@ def test_a_portion_sizer_shrinks_to_budget_and_learns_from_what_answered() -> No
     assert sizer.budget == 300.0
     sizer.observe({"y": {}, "z": {}}, scan.PORTION_FIXED_SECONDS + 20.0, answered=True)  # 0.1 s per visit
     assert 450 < sizer.budget < 550, sizer.budget
+    # A portion that finished inside the fixed start says nothing: the budget must not move on it.
+    before = sizer.budget
+    sizer.observe({"y": {}}, scan.PORTION_FIXED_SECONDS + 1.0, answered=True)
+    assert sizer.budget == before
+    # And a genuinely cheap portion may double the budget, never more: 0.01 s per visit would fit 5,000.
+    sizer.observe({"w": {}}, scan.PORTION_FIXED_SECONDS + 5.0 + 5.0, answered=True)
+    assert sizer.budget == before * scan.PORTION_MAX_GROWTH, sizer.budget