diff --git a/rpcc/conn.go b/rpcc/conn.go
index aa210df..4482582 100644
--- a/rpcc/conn.go
+++ b/rpcc/conn.go
@@ -240,18 +240,17 @@ type Conn struct {
 	compressionLevel func(level int) error
 
 	mu      sync.Mutex // Protects following.
-	closed  bool
 	reqSeq  uint64
 	pending map[uint64]*rpcCall
+	streams map[string]*streamClients
+	closed  bool
+	err     error // Protected by mu and closed until context is cancelled.
 
 	reqMu sync.Mutex // Protects following.
 	req   Request
 	// Encodes and decodes JSON onto conn. Encoding is
 	// guarded by mutex and decoding is done by recv.
 	codec Codec
-
-	streamMu sync.Mutex // Protects following.
-	streams  map[string]*streamClients
 }
 
 // Response represents an RPC response or notification sent by the server.
@@ -378,7 +377,7 @@ func (c *Conn) send(ctx context.Context, call *rpcCall) (err error) {
 	c.mu.Lock()
 	if c.closed {
 		c.mu.Unlock()
-		return ErrConnClosing
+		return c.err
 	}
 	c.reqSeq++
 	reqID := c.reqSeq
@@ -421,26 +420,25 @@ func (c *Conn) send(ctx context.Context, call *rpcCall) (err error) {
 // notify handles RPC notifications and sends them
 // to the appropriate stream listeners.
 func (c *Conn) notify(method string, data []byte) {
-	c.streamMu.Lock()
+	c.mu.Lock()
 	stream := c.streams[method]
-	c.streamMu.Unlock()
-
 	if stream != nil {
 		// Stream writer must be able to handle incoming writes
 		// even after it has been removed (unsubscribed).
 		stream.write(method, data)
 	}
+	c.mu.Unlock()
 }
 
 // listen registers a new stream listener (chan) for the RPC notification
 // method. Returns a function for removing the listener. Error if the
 // connection is closed.
 func (c *Conn) listen(method string, w streamWriter) (func(), error) {
-	c.streamMu.Lock()
-	defer c.streamMu.Unlock()
+	c.mu.Lock()
+	defer c.mu.Unlock()
 
 	if c.streams == nil {
-		return nil, ErrConnClosing
+		return nil, c.err
 	}
 
 	stream, ok := c.streams[method]
@@ -454,35 +452,59 @@ func (c *Conn) listen(method string, w streamWriter) (func(), error) {
 	return unsub, nil
 }
 
-// Close closes the connection.
-func (c *Conn) close(err error) error {
-	c.cancel()
+type closeError struct {
+	msg string
+	err error
+}
+
+func (e *closeError) Cause() error {
+	return e.err
+}
+
+func (e *closeError) Error() string {
+	return fmt.Sprintf("%s: %v", e.msg, e.err)
+}
 
+// Close closes the connection. Subsequent calls to Close will return the error
+// that closed the connection.
+func (c *Conn) close(err error) error {
 	c.mu.Lock()
+	defer c.mu.Unlock()
+
 	if c.closed {
-		c.mu.Unlock()
-		return ErrConnClosing
+		return c.err
 	}
 	c.closed = true
 	if err == nil {
 		err = ErrConnClosing
+	} else {
+		err = &closeError{msg: ErrConnClosing.Error(), err: err}
 	}
+	c.err = err
 	for id, call := range c.pending {
 		delete(c.pending, id)
 		call.done(err)
 	}
-	c.mu.Unlock()
-
-	// Stop sending on all streams.
-	c.streamMu.Lock()
+	// Stop sending on all streams by signaling
+	// that the connection is closed.
 	c.streams = nil
-	c.streamMu.Unlock()
 
 	// Conn can be nil if DialContext did not complete.
 	if c.conn != nil {
-		err = c.conn.Close()
+		wserr := c.conn.Close()
+		if wserr != nil && err == ErrConnClosing {
+			err = wserr
+			c.err = &closeError{msg: ErrConnClosing.Error(), err: err}
+		}
 	}
 
+	// Delay cancel until c.err has settled, at this point any active
+	// streams will be closed.
+	c.cancel()
+
+	if err == ErrConnClosing {
+		return nil
+	}
 	return err
 }
 
diff --git a/rpcc/conn_test.go b/rpcc/conn_test.go
index 0cc4b3b..1450830 100644
--- a/rpcc/conn_test.go
+++ b/rpcc/conn_test.go
@@ -339,6 +339,60 @@ func TestConn_StreamRecv(t *testing.T) {
 	}
 }
 
+func TestConn_PropagateError(t *testing.T) {
+	srv := newTestServer(t, nil)
+	defer srv.Close()
+
+	ctx, cancel := context.WithCancel(context.Background())
+	defer cancel()
+
+	s1, err := NewStream(ctx, "test.Stream1", srv.conn)
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer s1.Close()
+	s2, err := NewStream(ctx, "test.Stream2", srv.conn)
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer s2.Close()
+
+	errC := make(chan error, 2)
+	go func() {
+		errC <- Invoke(ctx, "test.Invoke", nil, nil, srv.conn)
+	}()
+	go func() {
+		var reply string
+		errC <- s1.RecvMsg(&reply)
+	}()
+
+	// Give a little time for both Invoke & Recv.
+	time.Sleep(5 * time.Millisecond)
+
+	srv.wsConn.Close()
+
+	// Give a little time for connection to close.
+	time.Sleep(5 * time.Millisecond)
+
+	lastErr := Invoke(ctx, "test.Invoke", nil, nil, srv.conn)
+	if lastErr == nil {
+		t.Error("RecvMsg on closed connection: got nil, want an error")
+	}
+
+	var reply string
+	err = s2.RecvMsg(&reply)
+	if err != lastErr {
+		t.Errorf("Error was not repeated, got %v, want %v", err, lastErr)
+	}
+
+	for i := 0; i < 2; i++ {
+		err := <-errC
+		if err != lastErr {
+			t.Errorf("Error was not repeated, got %v, want %v", err, lastErr)
+		}
+	}
+}
+
 func TestConn_Context(t *testing.T) {
 	srv := newTestServer(t, nil)
 	defer srv.Close()
diff --git a/rpcc/stream.go b/rpcc/stream.go
index 507d2c4..367c147 100644
--- a/rpcc/stream.go
+++ b/rpcc/stream.go
@@ -172,7 +172,7 @@ func (s *streamClient) watch() {
 	case <-s.ctx.Done():
 		s.close(s.ctx.Err())
 	case <-s.conn.ctx.Done():
-		s.close(ErrConnClosing)
+		s.close(s.conn.err)
 	case <-s.done:
 	}
 }
diff --git a/rpcc/stream_test.go b/rpcc/stream_test.go
index 7d25007..2758e02 100644
--- a/rpcc/stream_test.go
+++ b/rpcc/stream_test.go
@@ -198,7 +198,7 @@ func TestStream_RecvAfterConnClose(t *testing.T) {
 	conn.notify("test", []byte(`"message2"`))
 	conn.notify("test", []byte(`"message3"`))
 
-	connCancel()
+	conn.Close()
 
 	for i := 0; i < 3; i++ {
 		var reply string
@@ -210,7 +210,7 @@ func TestStream_RecvAfterConnClose(t *testing.T) {
 
 	err = s.RecvMsg(nil)
 	if err != ErrConnClosing {
-		t.Errorf("err got %v, want ErrConnClosing", err)
+		t.Errorf("err got %v, want %v", err, ErrConnClosing)
 	}
 }