diff --git a/errors.go b/errors.go
index 5ffc742..7bedec5 100644
--- a/errors.go
+++ b/errors.go
@@ -64,7 +64,7 @@ var (
 
 	// ErrSessionShutdown is used if there is a shutdown during
 	// an operation
-	ErrSessionShutdown = &Error{msg: "session shutdown"}
+	ErrSessionShutdown = &GoAwayError{ErrorCode: goAwayNormal, Remote: false}
 
 	// ErrStreamsExhausted is returned if we have no more
 	// stream ids to issue
@@ -87,7 +87,7 @@ var (
 	ErrUnexpectedFlag = &Error{msg: "unexpected flag"}
 
 	// ErrRemoteGoAway is used when we get a go away from the other side
-	ErrRemoteGoAway = &Error{msg: "remote end is not accepting connections"}
+	ErrRemoteGoAway = &GoAwayError{Remote: true, ErrorCode: goAwayNormal}
 
 	// ErrStreamReset is sent if a stream is reset. This can happen
 	// if the backlog is exceeded, or if there was a remote GoAway.
diff --git a/session.go b/session.go
index 62ea2c3..3a62ac2 100644
--- a/session.go
+++ b/session.go
@@ -102,6 +102,8 @@ type Session struct {
 	// recvDoneCh is closed when recv() exits to avoid a race
 	// between stream registration and stream shutdown
 	recvDoneCh chan struct{}
+	// recvErr is the error the receive loop ended with
+	recvErr error
 
 	// sendDoneCh is closed when send() exits to avoid a race
 	// between returning from a Stream.Write and exiting from the send loop
@@ -288,10 +290,18 @@ func (s *Session) AcceptStream() (*Stream, error) {
 // 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)
+	return s.closeWithGoAway(goAwayNormal)
 }
 
-func (s *Session) close(sendGoAway bool, errCode uint32) error {
+// CloseWithError is used to close the session and all streams after sending a GoAway message with errCode.
+// 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) CloseWithError(errCode uint32) error {
+	return s.closeWithGoAway(errCode)
+}
+
+func (s *Session) closeWithGoAway(errCode uint32) error {
 	s.shutdownLock.Lock()
 	defer s.shutdownLock.Unlock()
 
@@ -300,22 +310,25 @@ func (s *Session) close(sendGoAway bool, errCode uint32) error {
 	}
 	s.shutdown = true
 	if s.shutdownErr == nil {
-		s.shutdownErr = ErrSessionShutdown
+		if errCode == goAwayNormal {
+			s.shutdownErr = ErrSessionShutdown
+		} else {
+			s.shutdownErr = &GoAwayError{Remote: false, ErrorCode: errCode}
+		}
 	}
 	close(s.shutdownCh)
 	s.stopKeepalive()
 
 	// wait for write loop to exit
-	_ = s.conn.SetWriteDeadline(time.Now().Add(-1 * time.Hour)) // if SetWriteDeadline errored, any blocked writes will be unblocked
+	// We need to complete writing the current frame before sending a goaway
+	// This will wait for at most s.config.ConnectionWriteTimeout
 	<-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
-		}
+	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
 
@@ -329,15 +342,30 @@ func (s *Session) close(sendGoAway bool, errCode uint32) error {
 	return nil
 }
 
-// exitErr is used to handle an error that is causing the
-// session to terminate.
-func (s *Session) exitErr(err error) {
+func (s *Session) closeWithoutGoAway(err error) error {
 	s.shutdownLock.Lock()
+	defer s.shutdownLock.Unlock()
+	if s.shutdown {
+		return nil
+	}
+	s.shutdown = true
 	if s.shutdownErr == nil {
 		s.shutdownErr = err
 	}
-	s.shutdownLock.Unlock()
-	s.close(false, 0)
+	close(s.shutdownCh)
+	s.conn.Close()
+	<-s.sendDoneCh
+	<-s.recvDoneCh
+	s.stopKeepalive()
+
+	s.streamLock.Lock()
+	defer s.streamLock.Unlock()
+	for id, stream := range s.streams {
+		stream.forceClose()
+		delete(s.streams, id)
+		stream.memorySpan.Done()
+	}
+	return nil
 }
 
 // GoAway can be used to prevent accepting further
@@ -468,7 +496,7 @@ func (s *Session) startKeepalive() {
 
 		if err != nil {
 			s.logger.Printf("[ERR] yamux: keepalive failed: %v", err)
-			s.exitErr(ErrKeepAliveTimeout)
+			s.closeWithoutGoAway(ErrKeepAliveTimeout)
 		}
 	})
 }
@@ -533,7 +561,20 @@ func (s *Session) sendMsg(hdr header, body []byte, deadline <-chan struct{}) err
 // send is a long running goroutine that sends data
 func (s *Session) send() {
 	if err := s.sendLoop(); err != nil {
-		s.exitErr(err)
+		// Prefer the recvLoop error over the sendLoop error. The receive loop might have the error code
+		// received in a GoAway frame received just before the TCP RST that closed the sendLoop
+		s.shutdownLock.Lock()
+		if s.shutdownErr == nil {
+			s.conn.Close()
+			<-s.recvDoneCh
+			if _, ok := s.recvErr.(*GoAwayError); ok {
+				s.shutdownErr = s.recvErr
+			} else {
+				s.shutdownErr = err
+			}
+		}
+		s.shutdownLock.Unlock()
+		s.closeWithoutGoAway(err)
 	}
 }
 
@@ -661,7 +702,7 @@ func (s *Session) sendLoop() (err error) {
 // recv is a long running goroutine that accepts new data
 func (s *Session) recv() {
 	if err := s.recvLoop(); err != nil {
-		s.exitErr(err)
+		s.closeWithoutGoAway(err)
 	}
 }
 
@@ -683,7 +724,10 @@ func (s *Session) recvLoop() (err error) {
 			err = fmt.Errorf("panic in yamux receive loop: %s", rerr)
 		}
 	}()
-	defer close(s.recvDoneCh)
+	defer func() {
+		s.recvErr = err
+		close(s.recvDoneCh)
+	}()
 	var hdr header
 	for {
 		// fmt.Printf("ReadFull from %#v\n", s.reader)
@@ -799,17 +843,17 @@ func (s *Session) handleGoAway(hdr header) error {
 	switch code {
 	case goAwayNormal:
 		atomic.SwapInt32(&s.remoteGoAway, 1)
+		// Don't close connection on normal go away. Let the existing streams
+		// complete gracefully.
+		return nil
 	case goAwayProtoErr:
 		s.logger.Printf("[ERR] yamux: received protocol error go away")
-		return fmt.Errorf("yamux protocol error")
 	case goAwayInternalErr:
 		s.logger.Printf("[ERR] yamux: received internal error go away")
-		return fmt.Errorf("remote yamux internal error")
 	default:
-		s.logger.Printf("[ERR] yamux: received unexpected go away")
-		return fmt.Errorf("unexpected go away received")
+		s.logger.Printf("[ERR] yamux: received go away with error code: %d", code)
 	}
-	return nil
+	return &GoAwayError{Remote: true, ErrorCode: code}
 }
 
 // incomingStream is used to create a new incoming stream
diff --git a/session_test.go b/session_test.go
index 974b6d5..df3e3c9 100644
--- a/session_test.go
+++ b/session_test.go
@@ -3,6 +3,7 @@ package yamux
 import (
 	"bytes"
 	"context"
+	"errors"
 	"fmt"
 	"io"
 	"math/rand"
@@ -39,6 +40,8 @@ type pipeConn struct {
 	writeDeadline pipeDeadline
 	writeBlocker  chan struct{}
 	closeCh       chan struct{}
+	closeOnce     sync.Once
+	closeErr      error
 }
 
 func (p *pipeConn) SetDeadline(t time.Time) error {
@@ -65,10 +68,12 @@ func (p *pipeConn) Write(b []byte) (int, error) {
 }
 
 func (p *pipeConn) Close() error {
-	p.writeDeadline.set(time.Time{})
-	err := p.Conn.Close()
-	close(p.closeCh)
-	return err
+	p.closeOnce.Do(func() {
+		p.writeDeadline.set(time.Time{})
+		p.closeErr = p.Conn.Close()
+		close(p.closeCh)
+	})
+	return p.closeErr
 }
 
 func (p *pipeConn) BlockWrites() {
@@ -650,6 +655,35 @@ func TestGoAway(t *testing.T) {
 		default:
 			t.Fatalf("err: %v", err)
 		}
+		time.Sleep(50 * time.Millisecond)
+	}
+	t.Fatalf("expected GoAway error")
+}
+
+func TestCloseWithError(t *testing.T) {
+	// This test is noisy.
+	conf := testConf()
+	conf.LogOutput = io.Discard
+
+	client, server := testClientServerConfig(conf)
+	defer client.Close()
+	defer server.Close()
+
+	if err := server.CloseWithError(42); err != nil {
+		t.Fatalf("err: %v", err)
+	}
+
+	for i := 0; i < 100; i++ {
+		s, err := client.Open(context.Background())
+		if err == nil {
+			s.Close()
+			time.Sleep(50 * time.Millisecond)
+			continue
+		}
+		if !errors.Is(err, &GoAwayError{ErrorCode: 42, Remote: true}) {
+			t.Fatalf("err: %v", err)
+		}
+		return
 	}
 	t.Fatalf("expected GoAway error")
 }
@@ -1048,6 +1082,7 @@ func TestKeepAlive_Timeout(t *testing.T) {
 	// Prevent the client from responding
 	clientConn := client.conn.(*pipeConn)
 	clientConn.BlockWrites()
+	defer clientConn.UnblockWrites()
 
 	select {
 	case err := <-errCh: