diff --git a/cmd/mesh-controller/delivery_integration_test.go b/cmd/mesh-controller/delivery_integration_test.go
index a50bf4ec..fa0c04cf 100644
--- a/cmd/mesh-controller/delivery_integration_test.go
+++ b/cmd/mesh-controller/delivery_integration_test.go
@@ -72,7 +72,10 @@ func TestAMergeWaitsForItsDeliverysWordAndThePersonsWordWorksWithoutIt(t *testin
 	}
 
 	// No holder on record: the merge starts its walk, as before.
+	// A cut takes its first tier from the builder's keys and a step of the walk records the take (the walk asks no
+	// build), so each walk that starts is stepped once before its takes are counted.
 	p := merge("c1aaaaaaaa", "modules/app/index.ts")
+	advanceHeld(ctx, open)
 	if p.Waiting() || len(*asked) != 1 {
 		t.Fatalf("with no holder on record the walk waited (%v) or asked %v", p.Waiting(), *asked)
 	}
@@ -116,6 +119,7 @@ func TestAMergeWaitsForItsDeliverysWordAndThePersonsWordWorksWithoutIt(t *testin
 	// ADR 0276): the merge's batch is cut once it ended.
 	finish(p.ID)
 	p = merge("c3cccccccc", "modules/mesh-delivery/main.go")
+	advanceHeld(ctx, open)
 	if p.Waiting() || len(*asked) != 3 {
 		t.Fatalf("mesh-delivery's own walk waited for mesh-delivery: %v %v", p.Waiting(), *asked)
 	}
@@ -157,7 +161,9 @@ func TestAMergeWaitsForItsDeliverysWordAndThePersonsWordWorksWithoutIt(t *testin
 		t.Fatal(err)
 	}
 	asks := len(*asked)
-	if p = merge("c6ffffffff", "modules/app/index.ts"); p.Waiting() || len(*asked) != asks+1 {
+	p = merge("c6ffffffff", "modules/app/index.ts")
+	advanceHeld(ctx, open)
+	if p.Waiting() || len(*asked) != asks+1 {
 		t.Fatalf("with the holder gone the walk waited: %v", p.Waiting())
 	}
 }