diff --git a/go.mod b/go.mod
index 1730ffa36d..fc9c2b8640 100644
--- a/go.mod
+++ b/go.mod
@@ -33,7 +33,7 @@ require (
 	github.com/libp2p/zeroconf/v2 v2.2.0
 	github.com/lucas-clemente/quic-go v0.31.0
 	github.com/marten-seemann/tcp v0.0.0-20210406111302-dfbc87cc63fd
-	github.com/marten-seemann/webtransport-go v0.2.0
+	github.com/marten-seemann/webtransport-go v0.3.0
 	github.com/mikioh/tcpinfo v0.0.0-20190314235526-30a79bb1804b
 	github.com/minio/sha256-simd v1.0.0
 	github.com/mr-tron/base58 v1.2.0
diff --git a/go.sum b/go.sum
index ec35b6a159..37a7db8fef 100644
--- a/go.sum
+++ b/go.sum
@@ -333,8 +333,8 @@ github.com/marten-seemann/qtls-go1-19 v0.1.1 h1:mnbxeq3oEyQxQXwI4ReCgW9DPoPR94sN
 github.com/marten-seemann/qtls-go1-19 v0.1.1/go.mod h1:5HTDWtVudo/WFsHKRNuOhWlbdjrfs5JHrYb0wIJqGpI=
 github.com/marten-seemann/tcp v0.0.0-20210406111302-dfbc87cc63fd h1:br0buuQ854V8u83wA0rVZ8ttrq5CpaPZdvrK0LP2lOk=
 github.com/marten-seemann/tcp v0.0.0-20210406111302-dfbc87cc63fd/go.mod h1:QuCEs1Nt24+FYQEqAAncTDPJIuGs+LxK1MCiFL25pMU=
-github.com/marten-seemann/webtransport-go v0.2.0 h1:987jPVqcyE3vF+CHNIxDhT0P21O+bI4fVF+0NoRujSo=
-github.com/marten-seemann/webtransport-go v0.2.0/go.mod h1:XmnWYsWXaxUF7kjeIIzLWPyS+q0OcBY5vA64NuyK0ps=
+github.com/marten-seemann/webtransport-go v0.3.0 h1:TqUSf7/qZN8bJyuGrDMz9nDrfMbgH8p7KqV3TYrkBgo=
+github.com/marten-seemann/webtransport-go v0.3.0/go.mod h1:4xcfySgZMLP4aG5GBGj1egP7NlpfwgYJ1WJMvPPiVMU=
 github.com/mattn/go-isatty v0.0.14/go.mod h1:7GGIvUiUoEMVVmxf/4nioHXj79iQHKdU27kJ6hsGG94=
 github.com/mattn/go-isatty v0.0.16 h1:bq3VjFmv/sOjHtdEhmkEV4x1AJtvUvOJ2PFAZ5+peKQ=
 github.com/mattn/go-isatty v0.0.16/go.mod h1:kYGgaQfpe5nmfYZH+SKPsOc2e4SrIfOl2e/yFXSvRLM=
diff --git a/p2p/transport/webtransport/conn.go b/p2p/transport/webtransport/conn.go
index d8a366a0eb..4886a2c501 100644
--- a/p2p/transport/webtransport/conn.go
+++ b/p2p/transport/webtransport/conn.go
@@ -69,7 +69,7 @@ func (c *conn) allowWindowIncrease(size uint64) bool {
 // garbage collection to properly work in this package.
 func (c *conn) Close() error {
 	c.transport.removeConn(c.session)
-	return c.session.Close()
+	return c.session.CloseWithError(0, "")
 }
 
 func (c *conn) IsClosed() bool           { return c.session.Context().Err() != nil }
diff --git a/p2p/transport/webtransport/listener.go b/p2p/transport/webtransport/listener.go
index 9a93d014b1..03ff72f81c 100644
--- a/p2p/transport/webtransport/listener.go
+++ b/p2p/transport/webtransport/listener.go
@@ -137,7 +137,7 @@ func (l *listener) httpHandler(w http.ResponseWriter, r *http.Request) {
 	if err != nil {
 		cancel()
 		log.Debugw("handshake failed", "error", err)
-		sess.Close()
+		sess.CloseWithError(1, "")
 		connScope.Done()
 		return
 	}
@@ -145,14 +145,14 @@ func (l *listener) httpHandler(w http.ResponseWriter, r *http.Request) {
 
 	if l.transport.gater != nil && !l.transport.gater.InterceptSecured(network.DirInbound, sconn.RemotePeer(), sconn) {
 		// TODO: can we close with a specific error here?
-		sess.Close()
+		sess.CloseWithError(errorCodeConnectionGating, "")
 		connScope.Done()
 		return
 	}
 
 	if err := connScope.SetPeer(sconn.RemotePeer()); err != nil {
 		log.Debugw("resource manager blocked incoming connection for peer", "peer", sconn.RemotePeer(), "addr", r.RemoteAddr, "error", err)
-		sess.Close()
+		sess.CloseWithError(1, "")
 		connScope.Done()
 		return
 	}
@@ -163,7 +163,7 @@ func (l *listener) httpHandler(w http.ResponseWriter, r *http.Request) {
 	case l.queue <- conn:
 	default:
 		log.Debugw("accept queue full, dropping incoming connection", "peer", sconn.RemotePeer(), "addr", r.RemoteAddr, "error", err)
-		sess.Close()
+		sess.CloseWithError(1, "")
 		connScope.Done()
 	}
 }
diff --git a/p2p/transport/webtransport/stream.go b/p2p/transport/webtransport/stream.go
index ff17b3083f..623fc6036f 100644
--- a/p2p/transport/webtransport/stream.go
+++ b/p2p/transport/webtransport/stream.go
@@ -10,7 +10,7 @@ import (
 )
 
 const (
-	reset webtransport.ErrorCode = 0
+	reset webtransport.StreamErrorCode = 0
 )
 
 type webtransportStream struct {
diff --git a/p2p/transport/webtransport/transport.go b/p2p/transport/webtransport/transport.go
index bfb8adb3bf..0b133e08fd 100644
--- a/p2p/transport/webtransport/transport.go
+++ b/p2p/transport/webtransport/transport.go
@@ -34,6 +34,8 @@ var log = logging.Logger("webtransport")
 
 const webtransportHTTPEndpoint = "/.well-known/libp2p-webtransport"
 
+const errorCodeConnectionGating = 0x47415445 // GATE in ASCII
+
 const certValidity = 14 * 24 * time.Hour
 
 type Option func(*transport) error
@@ -153,13 +155,12 @@ func (t *transport) Dial(ctx context.Context, raddr ma.Multiaddr, p peer.ID) (tp
 	}
 	sconn, err := t.upgrade(ctx, sess, p, certHashes)
 	if err != nil {
-		sess.Close()
+		sess.CloseWithError(1, "")
 		scope.Done()
 		return nil, err
 	}
 	if t.gater != nil && !t.gater.InterceptSecured(network.DirOutbound, p, sconn) {
-		// TODO: can we close with a specific error here?
-		sess.Close()
+		sess.CloseWithError(errorCodeConnectionGating, "")
 		scope.Done()
 		return nil, fmt.Errorf("secured connection gated")
 	}