diff --git a/internal/discriminator/routewatchtags_test.go b/internal/discriminator/routewatchtags_test.go
index 33327c9..4b3e41b 100644
--- a/internal/discriminator/routewatchtags_test.go
+++ b/internal/discriminator/routewatchtags_test.go
@@ -153,14 +153,10 @@ func TestUnsetRouteWatchChangesNothing(t *testing.T) {
 func TestUnreachableRouteWatchLetsTheRequestThroughAndSaysWhy(t *testing.T) {
 	t.Parallel()
 
-	// A stand-in that is closed at once, so that the port refuses connections.
-	dead := httptest.NewServer(http.NotFoundHandler())
-	url := dead.URL
-
-	dead.Close()
-
+	// Another test can take a closed server's port at once, so routewatch's
+	// address here is a multicast address, to which TCP cannot connect.
 	s, _, _ := startWithClock(t, "", map[string]string{
-		lookupSource: off, routeWatchURL: url,
+		lookupSource: off, routeWatchURL: "http://224.0.0.1",
 	})
 
 	wantTagsMissing(t, s.get(fromDE, http.StatusOK, requestlog.ActionForward),
diff --git a/internal/routewatch/routewatch_test.go b/internal/routewatch/routewatch_test.go
index 60c197a..c74b1af 100644
--- a/internal/routewatch/routewatch_test.go
+++ b/internal/routewatch/routewatch_test.go
@@ -239,12 +239,17 @@ func TestAnswerRoutewatchCannotBeTakenFromFails(t *testing.T) {
 	}
 }
 
-func TestRefusedConnectionFailsTheQueryAndTheLogOmitsTheClient(t *testing.T) {
+func TestUnreachableRoutewatchFailsTheQueryAndTheLogOmitsTheClient(t *testing.T) {
 	t.Parallel()
 
 	f := newFixture(t, answering(routedAnswer))
 
-	f.server.Close()
+	// Another test can take a closed server's port at once, so routewatch's
+	// address here is a multicast address, to which TCP cannot connect.
+	f.client = routewatch.New(routewatch.Params{
+		URL: "http://224.0.0.1/", Now: f.clk.Now,
+		ProcessLog: slog.New(slog.NewTextHandler(f.log, nil)),
+	})
 
 	f.route()
 	f.waitFor(routewatch.RequestFailed)
diff --git a/internal/sww/sww_test.go b/internal/sww/sww_test.go
index 8638cfa..3087637 100644
--- a/internal/sww/sww_test.go
+++ b/internal/sww/sww_test.go
@@ -975,9 +975,20 @@ func TestStalledRemoteLogEndpointHoldsUpNoRequest(t *testing.T) {
 			t.Errorf("no line dropped in the metrics:\n%s", metrics)
 		}
 
-		// Closed, the endpoint refuses the connection made to send the
-		// lines still waiting at the stop, which then does not wait.
-		_ = endpoint.Close()
+		// From here the endpoint closes each connection it takes, so the
+		// one made to send the lines still waiting at the stop fails at
+		// once. Closing the endpoint instead would free its port for
+		// another test to take.
+		go func() {
+			for {
+				conn, err := endpoint.Accept()
+				if err != nil {
+					return
+				}
+
+				_ = conn.Close()
+			}
+		}()
 	})
 
 	out.line(t, "type", "request")