diff --git a/transport.go b/transport.go
index 7590be32..34e0b21c 100644
--- a/transport.go
+++ b/transport.go
@@ -177,8 +177,6 @@ func (t *Transport) DialEarly(ctx context.Context, addr net.Addr, tlsConf *tls.C
 
 func (t *Transport) init(isServer bool) error {
 	t.initOnce.Do(func() {
-		getMultiplexer().AddConn(t.Conn)
-
 		var conn rawConn
 		if c, ok := t.Conn.(rawConn); ok {
 			conn = c
@@ -212,6 +210,7 @@ func (t *Transport) init(isServer bool) error {
 			t.connIDGenerator = &protocol.DefaultConnectionIDGenerator{ConnLen: t.connIDLen}
 		}
 
+		getMultiplexer().AddConn(t.Conn)
 		go t.listen(conn)
 		go t.runSendQueue()
 	})
diff --git a/transport_test.go b/transport_test.go
index c78742f8..f46affb3 100644
--- a/transport_test.go
+++ b/transport_test.go
@@ -6,6 +6,7 @@ import (
 	"crypto/tls"
 	"errors"
 	"net"
+	"syscall"
 	"time"
 
 	mocklogging "github.com/quic-go/quic-go/internal/mocks/logging"
@@ -307,4 +308,27 @@ var _ = Describe("Transport", func() {
 		pconn.EXPECT().Close()
 		Expect(tr.Close()).To(Succeed())
 	})
+
+	It("doesn't add the PacketConn to the multiplexer if (*Transport).init fails", func() {
+		packetChan := make(chan packetToRead)
+		pconn := newMockPacketConn(packetChan)
+		syscallconn := &mockSyscallConn{pconn}
+
+		tr := &Transport{
+			Conn: syscallconn,
+		}
+
+		err := tr.init(false)
+		Expect(err).To(HaveOccurred())
+		conns := getMultiplexer().(*connMultiplexer).conns
+		Expect(len(conns)).To(BeZero())
+	})
 })
+
+type mockSyscallConn struct {
+	net.PacketConn
+}
+
+func (c *mockSyscallConn) SyscallConn() (syscall.RawConn, error) {
+	return nil, errors.New("mocked")
+}