diff --git a/internal/httpfetcher/max_connections_internal_test.go b/internal/httpfetcher/max_connections_internal_test.go
index a19437f..a776460 100644
--- a/internal/httpfetcher/max_connections_internal_test.go
+++ b/internal/httpfetcher/max_connections_internal_test.go
@@ -153,9 +153,11 @@ func TestFetchRemovesIdleHostSemaphores(t *testing.T) {
 }
 
 // TestFetchRemovesHostSemaphoreWhenNoConnection checks that a fetch that
-// ends without a connection leaves no semaphore behind, both when it is
-// refused after waiting for a connection shared by all hosts and when its
-// context ends while it waits for its host's slot.
+// ends without a connection leaves no semaphore behind: when it is refused
+// after waiting for a connection shared by all hosts, when its context ends
+// while it waits for its host's slot, and when its context ends while it
+// waits for a connection shared by all hosts, long before the 10 second
+// wait timeout.
 func TestFetchRemovesHostSemaphoreWhenNoConnection(t *testing.T) {
 	t.Parallel()
 
@@ -188,6 +190,18 @@ func TestFetchRemovesHostSemaphoreWhenNoConnection(t *testing.T) {
 			"want context.DeadlineExceeded", err)
 	}
 
+	// Back to the 10 second wait, so the next fetch's context ends first.
+	f.connectionWaitTimeout = ConnectionWaitTimeout
+
+	ctx, cancel = context.WithTimeout(t.Context(), 100*time.Millisecond)
+	defer cancel()
+
+	_, err = f.Fetch(ctx, imageURLOnPort(83))
+	if !errors.Is(err, context.DeadlineExceeded) {
+		t.Fatalf("Fetch() from a host with nothing open: error = %v, "+
+			"want context.DeadlineExceeded", err)
+	}
+
 	err = open.Content.Close()
 	if err != nil {
 		t.Fatalf("close first body: %v", err)