diff --git a/p2p/net/swarm/dial_ranker_test.go b/p2p/net/swarm/dial_ranker_test.go
index 81ceb28b82..f7a6172122 100644
--- a/p2p/net/swarm/dial_ranker_test.go
+++ b/p2p/net/swarm/dial_ranker_test.go
@@ -329,6 +329,13 @@ func TestDelayRankerOtherTransportDelay(t *testing.T) {
 				{Addr: onion1, Delay: 2*PublicQUICDelay + 2*PublicOtherDelay},
 			},
 		},
+		{
+			name:  "only-non-ip-addr",
+			addrs: []ma.Multiaddr{onion1},
+			output: []network.AddrDelay{
+				{Addr: onion1, Delay: PublicOtherDelay},
+			},
+		},
 	}
 	for _, tc := range testCase {
 		t.Run(tc.name, func(t *testing.T) {
diff --git a/p2p/test/basichost/basic_host_test.go b/p2p/test/basichost/basic_host_test.go
index 9cd442dbf0..ca7018d588 100644
--- a/p2p/test/basichost/basic_host_test.go
+++ b/p2p/test/basichost/basic_host_test.go
@@ -11,6 +11,7 @@ import (
 	"github.com/libp2p/go-libp2p/core/network"
 	"github.com/libp2p/go-libp2p/core/peer"
 	"github.com/libp2p/go-libp2p/core/peerstore"
+	"github.com/libp2p/go-libp2p/p2p/net/swarm"
 	"github.com/libp2p/go-libp2p/p2p/protocol/circuitv2/client"
 	"github.com/libp2p/go-libp2p/p2p/protocol/circuitv2/relay"
 	libp2pwebrtc "github.com/libp2p/go-libp2p/p2p/transport/webrtc"
@@ -199,3 +200,25 @@ func TestAddrFactorCertHashAppend(t *testing.T) {
 		return hasWebRTC && hasWebTransport
 	}, 5*time.Second, 100*time.Millisecond)
 }
+
+func TestWebRTCDirectDialDelay(t *testing.T) {
+	// This tests that only webrtc-direct dials are dialled immediately
+
+	h1, err := libp2p.New(
+		libp2p.Transport(libp2pwebrtc.New),
+		libp2p.ListenAddrStrings(
+			"/ip4/0.0.0.0/udp/0/webrtc-direct",
+		),
+	)
+	require.NoError(t, err)
+	h2, err := libp2p.New(
+		libp2p.Transport(libp2pwebrtc.New),
+		libp2p.NoListenAddrs,
+	)
+	require.NoError(t, err)
+
+	ctx, cancel := context.WithTimeout(context.Background(), swarm.PrivateOtherDelay)
+	defer cancel()
+	err = h2.Connect(ctx, peer.AddrInfo{ID: h1.ID(), Addrs: h1.Addrs()})
+	require.NoError(t, err)
+}