diff --git a/jsonrpc2.go b/jsonrpc2.go
index 4885b05..32bc98c 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
 
@@ -417,13 +416,29 @@ 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()
+
+	for _, call := range c.pending {
+		close(call.done)
+	}
+
+	if cause != nil && cause != io.EOF && cause != io.ErrUnexpectedEOF {
+		c.logger.Printf("jsonrpc2: protocol error: %v\n", cause)
+	}
+
+	close(c.disconnect)
+	c.closed = true
 	return c.stream.Close()
 }
 
@@ -436,7 +451,7 @@ 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 +690,7 @@ 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..b68f3c1 100644
--- a/jsonrpc2_test.go
+++ b/jsonrpc2_test.go
@@ -314,80 +314,82 @@ type noopHandler struct{}
 
 func (noopHandler) Handle(ctx context.Context, conn *jsonrpc2.Conn, req *jsonrpc2.Request) {}
 
-type readWriteCloser struct {
-	read, write func(p []byte) (n int, err error)
-}
+func TestConn_DisconnectNotify(t *testing.T) {
 
-func (x readWriteCloser) Read(p []byte) (n int, err error) {
-	return x.read(p)
-}
-
-func (x readWriteCloser) Write(p []byte) (n int, err error) {
-	return x.write(p)
-}
-
-func (readWriteCloser) Close() error { return nil }
-
-func eof(p []byte) (n int, err error) {
-	return 0, io.EOF
-}
-
-func TestConn_DisconnectNotify_EOF(t *testing.T) {
-	c := jsonrpc2.NewConn(context.Background(), jsonrpc2.NewBufferedStream(&readWriteCloser{eof, eof}, jsonrpc2.VarintObjectCodec{}), nil)
-	select {
-	case <-c.DisconnectNotify():
-	case <-time.After(200 * time.Millisecond):
-		t.Fatal("no disconnect notification")
-	}
-}
-
-func TestConn_DisconnectNotify_Close(t *testing.T) {
-	c := jsonrpc2.NewConn(context.Background(), jsonrpc2.NewBufferedStream(&readWriteCloser{eof, eof}, jsonrpc2.VarintObjectCodec{}), nil)
-	if err := c.Close(); err != nil {
-		t.Error(err)
-	}
-	select {
-	case <-c.DisconnectNotify():
-	case <-time.After(200 * time.Millisecond):
-		t.Fatal("no disconnect notification")
-	}
-}
-
-func TestConn_DisconnectNotify_Close_async(t *testing.T) {
-	done := make(chan struct{})
-	c := jsonrpc2.NewConn(context.Background(), jsonrpc2.NewBufferedStream(&readWriteCloser{eof, eof}, jsonrpc2.VarintObjectCodec{}), nil)
-	go func() {
-		if err := c.Close(); err != nil && err != jsonrpc2.ErrClosed {
+	t.Run("EOF", func(t *testing.T) {
+		connA, connB := net.Pipe()
+		c := jsonrpc2.NewConn(context.Background(), jsonrpc2.NewPlainObjectStream(connB), nil)
+		// By closing connA, connB receives io.EOF
+		if err := connA.Close(); err != nil {
 			t.Error(err)
 		}
-		close(done)
-	}()
-	select {
-	case <-c.DisconnectNotify():
-	case <-time.After(200 * time.Millisecond):
-		t.Fatal("no disconnect notification")
-	}
-	<-done
+		assertDisconnect(t, c, connB)
+	})
+
+	t.Run("Close", func(t *testing.T) {
+		_, connB := net.Pipe()
+		c := jsonrpc2.NewConn(context.Background(), jsonrpc2.NewPlainObjectStream(connB), nil)
+		if err := c.Close(); err != nil {
+			t.Error(err)
+		}
+		assertDisconnect(t, c, connB)
+	})
+
+	t.Run("Close async", func(t *testing.T) {
+		done := make(chan struct{})
+		_, connB := net.Pipe()
+		c := jsonrpc2.NewConn(context.Background(), jsonrpc2.NewPlainObjectStream(connB), nil)
+		go func() {
+			if err := c.Close(); err != nil && err != jsonrpc2.ErrClosed {
+				t.Error(err)
+			}
+			close(done)
+		}()
+		assertDisconnect(t, c, connB)
+		<-done
+	})
+
+	t.Run("protocol error", func(t *testing.T) {
+		connA, connB := net.Pipe()
+		c := jsonrpc2.NewConn(context.Background(), jsonrpc2.NewPlainObjectStream(connB), nil)
+		connA.Write([]byte("invalid json"))
+		assertDisconnect(t, c, connB)
+	})
 }
 
-func TestConn_Close_waitingForResponse(t *testing.T) {
-	c := jsonrpc2.NewConn(context.Background(), jsonrpc2.NewBufferedStream(&readWriteCloser{eof, eof}, jsonrpc2.VarintObjectCodec{}), noopHandler{})
-	done := make(chan struct{})
-	go func() {
-		if err := c.Call(context.Background(), "m", nil, nil); err != jsonrpc2.ErrClosed {
-			t.Errorf("got error %v, want %v", err, jsonrpc2.ErrClosed)
+func TestConn_Close(t *testing.T) {
+	t.Run("waiting for response", func(t *testing.T) {
+		connA, connB := net.Pipe()
+		nodeA := jsonrpc2.NewConn(
+			context.Background(),
+			jsonrpc2.NewPlainObjectStream(connA), noopHandler{},
+		)
+		defer nodeA.Close()
+		nodeB := jsonrpc2.NewConn(
+			context.Background(),
+			jsonrpc2.NewPlainObjectStream(connB),
+			noopHandler{},
+		)
+		defer nodeB.Close()
+
+		ready := make(chan struct{})
+		done := make(chan struct{})
+		go func() {
+			close(ready)
+			err := nodeB.Call(context.Background(), "m", nil, nil)
+			if err != jsonrpc2.ErrClosed {
+				t.Errorf("got error %v, want %v", err, jsonrpc2.ErrClosed)
+			}
+			close(done)
+		}()
+		// Wait for the request to be sent before we close the connection.
+		<-ready
+		if err := nodeB.Close(); err != nil && err != jsonrpc2.ErrClosed {
+			t.Error(err)
 		}
-		close(done)
-	}()
-	if err := c.Close(); err != nil && err != jsonrpc2.ErrClosed {
-		t.Error(err)
-	}
-	select {
-	case <-c.DisconnectNotify():
-	case <-time.After(200 * time.Millisecond):
-		t.Fatal("no disconnect notification")
-	}
-	<-done
+		assertDisconnect(t, nodeB, connB)
+		<-done
+	})
 }
 
 func serve(ctx context.Context, lis net.Listener, h jsonrpc2.Handler, streamMaker streamMaker, opts ...jsonrpc2.ConnOpt) error {
@@ -399,3 +401,17 @@ func serve(ctx context.Context, lis net.Listener, h jsonrpc2.Handler, streamMake
 		jsonrpc2.NewConn(ctx, streamMaker(conn), h, opts...)
 	}
 }
+
+func assertDisconnect(t *testing.T, c *jsonrpc2.Conn, conn io.Writer) {
+	select {
+	case <-c.DisconnectNotify():
+	case <-time.After(200 * time.Millisecond):
+		t.Fatal("no disconnect notification")
+	}
+	// Assert that conn is closed by trying to write to it.
+	_, got := conn.Write(nil)
+	want := io.ErrClosedPipe
+	if got != want {
+		t.Fatalf("got %q, want %q", got, want)
+	}
+}