diff --git a/modules/pier/reaper_test.go b/modules/pier/reaper_test.go
index 01e19897..e7a71f92 100644
--- a/modules/pier/reaper_test.go
+++ b/modules/pier/reaper_test.go
@@ -127,10 +127,13 @@ func TestSessionReaper(t *testing.T) {
 		if na, nb := a.pier().LocalSessions(), b.pier().LocalSessions(); na != 1 || nb != 1 {
 			t.Fatalf("local sessions while the record lives: A %d, B %d, want 1 and 1", na, nb)
 		}
+		// A request's state is persisted after its answer has been streamed;
+		// let the last ones finish before the record expires.
+		time.Sleep(100 * time.Millisecond)
 		mr.FastForward(31 * time.Minute)
 		// A pass that cannot read the store keeps the copy (asserted below),
-		// so a loaded host may need a second pass; the copy is reaped once.
-		reapAll := func(name string, in *instance) {
+		// so a loaded host may need a second pass.
+		reapAll := func(name string, in *instance) int {
 			t.Helper()
 			closed := 0
 			deadline := time.Now().Add(5 * time.Second)
@@ -140,12 +143,19 @@ func TestSessionReaper(t *testing.T) {
 				}
 				closed += in.pier().ReapNow(ctx)
 			}
-			if closed != 1 {
-				t.Fatalf("%s reaped %d sessions after the record expired, want 1", name, closed)
-			}
+			return closed
+		}
+		// B did not serve the last request: only the reaper can close its
+		// copy.
+		if closed := reapAll("B", b); closed != 1 {
+			t.Fatalf("B reaped %d sessions after the record expired, want 1", closed)
+		}
+		// A served it; a request of A's that finished after the expiry may
+		// close the copy first (persist finds the record gone), so A only
+		// has to hold no copy.
+		if closed := reapAll("A", a); closed > 1 {
+			t.Fatalf("A reaped %d sessions, want at most 1", closed)
 		}
-		reapAll("B", b)
-		reapAll("A", a)
 		if a.pier().LocalSessions() != 0 || b.pier().LocalSessions() != 0 {
 			t.Fatalf("copies left: A %d, B %d", a.pier().LocalSessions(), b.pier().LocalSessions())
 		}