diff --git a/jsonrpc2.go b/jsonrpc2.go
index 4885b05..b855390 100644
--- a/jsonrpc2.go
+++ b/jsonrpc2.go
@@ -366,11 +366,10 @@ type Conn struct {
 
 	h Handler
 
-	mu       sync.Mutex
-	shutdown bool
-	closing  bool
-	seq      uint64
-	pending  map[ID]*call
+	mu      sync.Mutex
+	closed  bool
+	seq     uint64
+	pending map[ID]*call
 
 	sending sync.Mutex
 
@@ -417,14 +416,35 @@ func NewConn(ctx context.Context, stream ObjectStream, h Handler, opts ...ConnOp
 // Close closes the JSON-RPC connection. The connection may not be
 // used after it has been closed.
 func (c *Conn) Close() error {
+	return c.close(nil)
+}
+
+func (c *Conn) close(cause error) error {
+	c.sending.Lock()
 	c.mu.Lock()
-	if c.shutdown || c.closing {
-		c.mu.Unlock()
+	defer c.sending.Unlock()
+	defer c.mu.Unlock()
+
+	if c.closed {
 		return ErrClosed
 	}
-	c.closing = true
-	c.mu.Unlock()
-	return c.stream.Close()
+
+	for _, call := range c.pending {
+		call.done <- cause
+		close(call.done)
+	}
+
+	if cause != nil && cause != io.EOF && cause != io.ErrUnexpectedEOF {
+		c.logger.Printf("jsonrpc2: protocol error: %v\n", cause)
+	}
+
+	if err := c.stream.Close(); err != nil {
+		return err
+	}
+
+	close(c.disconnect)
+	c.closed = true
+	return nil
 }
 
 func (c *Conn) send(_ context.Context, m *anyMessage, wait bool) (cc *call, err error) {
@@ -436,7 +456,7 @@ func (c *Conn) send(_ context.Context, m *anyMessage, wait bool) (cc *call, err
 	var id ID
 
 	c.mu.Lock()
-	if c.shutdown || c.closing {
+	if c.closed {
 		c.mu.Unlock()
 		return nil, ErrClosed
 	}
@@ -675,28 +695,7 @@ func (c *Conn) readMessages(ctx context.Context) {
 			}
 		}
 	}
-
-	c.sending.Lock()
-	c.mu.Lock()
-	c.shutdown = true
-	closing := c.closing
-	if err == io.EOF {
-		if closing {
-			err = ErrClosed
-		} else {
-			err = io.ErrUnexpectedEOF
-		}
-	}
-	for _, call := range c.pending {
-		call.done <- err
-		close(call.done)
-	}
-	c.mu.Unlock()
-	c.sending.Unlock()
-	if err != io.ErrUnexpectedEOF && !closing {
-		c.logger.Printf("jsonrpc2: protocol error: %v\n", err)
-	}
-	close(c.disconnect)
+	c.close(err)
 }
 
 // call represents a JSON-RPC call over its entire lifecycle.
diff --git a/jsonrpc2_test.go b/jsonrpc2_test.go
index ca600db..a8dec6e 100644
--- a/jsonrpc2_test.go
+++ b/jsonrpc2_test.go
@@ -390,6 +390,23 @@ func TestConn_Close_waitingForResponse(t *testing.T) {
 	<-done
 }
 
+func TestConn_DisconnectNotify_protocol_error(t *testing.T) {
+	connA, connB := net.Pipe()
+	c := jsonrpc2.NewConn(context.Background(), jsonrpc2.NewBufferedStream(connB, jsonrpc2.VarintObjectCodec{}), nil)
+	connA.Write([]byte("invalid json"))
+	select {
+	case <-c.DisconnectNotify():
+	case <-time.After(200 * time.Millisecond):
+		t.Fatal("no disconnect notification")
+	}
+	// Assert that the underlying connection is closed by trying to write to it.
+	_, got := connB.Write(nil)
+	want := io.ErrClosedPipe
+	if got != want {
+		t.Fatalf("got %q, want %q", got, want)
+	}
+}
+
 func serve(ctx context.Context, lis net.Listener, h jsonrpc2.Handler, streamMaker streamMaker, opts ...jsonrpc2.ConnOpt) error {
 	for {
 		conn, err := lis.Accept()