diff --git a/client.go b/client.go
index 35459a5..86b307b 100644
--- a/client.go
+++ b/client.go
@@ -111,7 +111,7 @@ func (c *Client) openStream(ctx context.Context) (net.Conn, error) {
 		if err != nil {
 			continue
 		}
-		stream, err = session.Open()
+		stream, err = session.OpenContext(ctx)
 		if err != nil {
 			continue
 		}
@@ -166,6 +166,8 @@ func (c *Client) offer(ctx context.Context) (abstractSession, error) {
 }
 
 func (c *Client) offerNew(ctx context.Context) (abstractSession, error) {
+	ctx, cancel := context.WithTimeout(ctx, TCPTimeout)
+	defer cancel()
 	conn, err := c.dialer.DialContext(ctx, N.NetworkTCP, Destination)
 	if err != nil {
 		return nil, err
@@ -190,7 +192,7 @@ func (c *Client) offerNew(ctx context.Context) (abstractSession, error) {
 		return nil, err
 	}
 	if c.brutal.Enabled {
-		err = c.brutalExchange(conn, session)
+		err = c.brutalExchange(ctx, conn, session)
 		if err != nil {
 			conn.Close()
 			session.Close()
@@ -201,8 +203,8 @@ func (c *Client) offerNew(ctx context.Context) (abstractSession, error) {
 	return session, nil
 }
 
-func (c *Client) brutalExchange(sessionConn net.Conn, session abstractSession) error {
-	stream, err := session.Open()
+func (c *Client) brutalExchange(ctx context.Context, sessionConn net.Conn, session abstractSession) error {
+	stream, err := session.OpenContext(ctx)
 	if err != nil {
 		return err
 	}
diff --git a/h2mux.go b/h2mux.go
index a67ef70..cb827a9 100644
--- a/h2mux.go
+++ b/h2mux.go
@@ -64,7 +64,7 @@ func (s *h2MuxServerSession) ServeHTTP(writer http.ResponseWriter, request *http
 	}
 }
 
-func (s *h2MuxServerSession) Open() (net.Conn, error) {
+func (s *h2MuxServerSession) OpenContext(ctx context.Context) (net.Conn, error) {
 	return nil, os.ErrInvalid
 }
 
@@ -197,13 +197,14 @@ func (s *h2MuxClientSession) MarkDead(conn *http2.ClientConn) {
 	s.Close()
 }
 
-func (s *h2MuxClientSession) Open() (net.Conn, error) {
+func (s *h2MuxClientSession) OpenContext(ctx context.Context) (net.Conn, error) {
 	pipeInReader, pipeInWriter := io.Pipe()
 	request := &http.Request{
 		Method: http.MethodConnect,
 		Body:   pipeInReader,
 		URL:    &url.URL{Scheme: "https", Host: "localhost"},
 	}
+	request = request.WithContext(ctx)
 	conn := newLateHTTPConn(pipeInWriter)
 	go func() {
 		response, err := s.transport.RoundTrip(request)
diff --git a/session.go b/session.go
index 2dc37b3..524f573 100644
--- a/session.go
+++ b/session.go
@@ -1,6 +1,7 @@
 package mux
 
 import (
+	"context"
 	"io"
 	"net"
 	"reflect"
@@ -12,7 +13,7 @@ import (
 )
 
 type abstractSession interface {
-	Open() (net.Conn, error)
+	OpenContext(ctx context.Context) (net.Conn, error)
 	Accept() (net.Conn, error)
 	NumStreams() int
 	Close() error
@@ -80,7 +81,7 @@ type smuxSession struct {
 	*smux.Session
 }
 
-func (s *smuxSession) Open() (net.Conn, error) {
+func (s *smuxSession) OpenContext(context.Context) (net.Conn, error) {
 	return s.OpenStream()
 }
 
@@ -96,6 +97,10 @@ type yamuxSession struct {
 	*yamux.Session
 }
 
+func (y *yamuxSession) OpenContext(context.Context) (net.Conn, error) {
+	return y.OpenStream()
+}
+
 func (y *yamuxSession) CanTakeNewRequest() bool {
 	return true
 }