diff --git a/conn.go b/conn.go
index 2ac19e9a..72f5df81 100644
--- a/conn.go
+++ b/conn.go
@@ -192,13 +192,6 @@ func newMaskKey() [4]byte {
 	return k
 }
 
-func hideTempErr(err error) error {
-	if e, ok := err.(net.Error); ok {
-		err = &netError{msg: e.Error(), timeout: e.Timeout()}
-	}
-	return err
-}
-
 func isControl(frameType int) bool {
 	return frameType == CloseMessage || frameType == PingMessage || frameType == PongMessage
 }
@@ -364,7 +357,6 @@ func (c *Conn) RemoteAddr() net.Addr {
 // Write methods
 
 func (c *Conn) writeFatal(err error) error {
-	err = hideTempErr(err)
 	c.writeErrMu.Lock()
 	if c.writeErr == nil {
 		c.writeErr = err
@@ -1033,7 +1025,7 @@ func (c *Conn) NextReader() (messageType int, r io.Reader, err error) {
 	for c.readErr == nil {
 		frameType, err := c.advanceFrame()
 		if err != nil {
-			c.readErr = hideTempErr(err)
+			c.readErr = err
 			break
 		}
 
@@ -1073,7 +1065,7 @@ func (r *messageReader) Read(b []byte) (int, error) {
 				b = b[:c.readRemaining]
 			}
 			n, err := c.br.Read(b)
-			c.readErr = hideTempErr(err)
+			c.readErr = err
 			if c.isServer {
 				c.readMaskPos = maskBytes(c.readMaskKey, c.readMaskPos, b[:n])
 			}
@@ -1096,7 +1088,7 @@ func (r *messageReader) Read(b []byte) (int, error) {
 		frameType, err := c.advanceFrame()
 		switch {
 		case err != nil:
-			c.readErr = hideTempErr(err)
+			c.readErr = err
 		case frameType == TextMessage || frameType == BinaryMessage:
 			c.readErr = errors.New("websocket: internal error, unexpected text or binary in Reader")
 		}
diff --git a/conn_test.go b/conn_test.go
index f0c29c39..3bd4f61b 100644
--- a/conn_test.go
+++ b/conn_test.go
@@ -814,3 +814,25 @@ func TestFormatMessageType(t *testing.T) {
 		t.Error("failed to format message type")
 	}
 }
+
+type fakeNetClosedReader struct {
+}
+
+func (r fakeNetClosedReader) Read([]byte) (int, error) {
+	return 0, net.ErrClosed
+}
+
+func TestConnectionClosed(t *testing.T) {
+	var b1, b2 bytes.Buffer
+
+	client := newTestConn(fakeNetClosedReader{}, &b1, false)
+	server := newTestConn(fakeNetClosedReader{}, &b2, true)
+
+	if _, _, err := server.NextReader(); !errors.Is(err, net.ErrClosed) {
+		t.Fatalf("server expects a net.ErrClosed error, %v returned", err)
+	}
+
+	if _, _, err := client.NextReader(); !errors.Is(err, net.ErrClosed) {
+		t.Fatalf("client expects a net.ErrClosed error, %v returned", err)
+	}
+}