diff --git a/const.go b/const.go
index c1a2deb..e737d85 100644
--- a/const.go
+++ b/const.go
@@ -3,6 +3,7 @@ package yamux
 import (
 	"encoding/binary"
 	"fmt"
+	"time"
 )
 
 const (
@@ -52,6 +53,7 @@ const (
 	// It's not an implementation choice, the value defined in the specification.
 	initialStreamWindow = 256 * 1024
 	maxStreamWindow     = 16 * 1024 * 1024
+	goAwayWaitTime      = 5 * time.Second
 )
 
 const (
diff --git a/session.go b/session.go
index c4cd1bd..62ea2c3 100644
--- a/session.go
+++ b/session.go
@@ -284,8 +284,14 @@ func (s *Session) AcceptStream() (*Stream, error) {
 }
 
 // Close is used to close the session and all streams.
-// Attempts to send a GoAway before closing the connection.
+// Attempts to send a GoAway before closing the connection. The GoAway may not actually be sent depending on the
+// semantics of the underlying net.Conn. For TCP connections, it may be dropped depending on LINGER value or
+// if there's unread data in the kernel receive buffer.
 func (s *Session) Close() error {
+	return s.close(true, goAwayNormal)
+}
+
+func (s *Session) close(sendGoAway bool, errCode uint32) error {
 	s.shutdownLock.Lock()
 	defer s.shutdownLock.Unlock()
 
@@ -297,10 +303,21 @@ func (s *Session) Close() error {
 		s.shutdownErr = ErrSessionShutdown
 	}
 	close(s.shutdownCh)
-	s.conn.Close()
 	s.stopKeepalive()
-	<-s.recvDoneCh
+
+	// wait for write loop to exit
+	_ = s.conn.SetWriteDeadline(time.Now().Add(-1 * time.Hour)) // if SetWriteDeadline errored, any blocked writes will be unblocked
 	<-s.sendDoneCh
+	if sendGoAway {
+		ga := s.goAway(errCode)
+		if err := s.conn.SetWriteDeadline(time.Now().Add(goAwayWaitTime)); err == nil {
+			_, _ = s.conn.Write(ga[:]) // there's nothing we can do on error here
+		}
+	}
+
+	s.conn.SetWriteDeadline(time.Time{})
+	s.conn.Close()
+	<-s.recvDoneCh
 
 	s.streamLock.Lock()
 	defer s.streamLock.Unlock()
@@ -320,7 +337,7 @@ func (s *Session) exitErr(err error) {
 		s.shutdownErr = err
 	}
 	s.shutdownLock.Unlock()
-	s.Close()
+	s.close(false, 0)
 }
 
 // GoAway can be used to prevent accepting further