diff --git a/jetty-websocket/jetty-websocket-tests/src/test/java/org/eclipse/jetty/websocket/tests/SingleOnMessageTest.java b/jetty-websocket/jetty-websocket-tests/src/test/java/org/eclipse/jetty/websocket/tests/SingleOnMessageTest.java
new file mode 100644
index 000000000000..492037ad6870
--- /dev/null
+++ b/jetty-websocket/jetty-websocket-tests/src/test/java/org/eclipse/jetty/websocket/tests/SingleOnMessageTest.java
@@ -0,0 +1,159 @@
+package org.eclipse.jetty.websocket.tests;
+
+import java.net.URI;
+import java.nio.ByteBuffer;
+import java.util.concurrent.CountDownLatch;
+import java.util.concurrent.TimeUnit;
+
+import org.eclipse.jetty.server.Server;
+import org.eclipse.jetty.server.ServerConnector;
+import org.eclipse.jetty.servlet.ServletContextHandler;
+import org.eclipse.jetty.util.BlockingArrayQueue;
+import org.eclipse.jetty.util.BufferUtil;
+import org.eclipse.jetty.websocket.api.RemoteEndpoint;
+import org.eclipse.jetty.websocket.api.Session;
+import org.eclipse.jetty.websocket.api.StatusCode;
+import org.eclipse.jetty.websocket.api.annotations.OnWebSocketClose;
+import org.eclipse.jetty.websocket.api.annotations.OnWebSocketConnect;
+import org.eclipse.jetty.websocket.api.annotations.OnWebSocketMessage;
+import org.eclipse.jetty.websocket.api.annotations.WebSocket;
+import org.eclipse.jetty.websocket.api.util.WSURI;
+import org.eclipse.jetty.websocket.client.WebSocketClient;
+import org.eclipse.jetty.websocket.server.NativeWebSocketServletContainerInitializer;
+import org.eclipse.jetty.websocket.server.WebSocketUpgradeFilter;
+import org.junit.jupiter.api.AfterEach;
+import org.junit.jupiter.api.BeforeEach;
+import org.junit.jupiter.api.Test;
+
+import static org.hamcrest.MatcherAssert.assertThat;
+import static org.hamcrest.Matchers.is;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+public class SingleOnMessageTest
+{
+    private final Server server = new Server();
+    private final WebSocketClient client = new WebSocketClient();
+    private final EventSocket serverSocket = new EventSocket();
+    private URI serverUri;
+
+    @BeforeEach
+    public void start() throws Exception
+    {
+        ServerConnector connector = new ServerConnector(server);
+        server.addConnector(connector);
+
+        ServletContextHandler contextHandler = new ServletContextHandler(ServletContextHandler.SESSIONS);
+        contextHandler.setContextPath("/");
+        NativeWebSocketServletContainerInitializer.configure(contextHandler,
+            (context, container) -> container.addMapping("/", (req, resp) -> serverSocket));
+        WebSocketUpgradeFilter.configure(contextHandler);
+
+        server.setHandler(contextHandler);
+        server.start();
+        serverUri = WSURI.toWebsocket(server.getURI());
+
+        client.start();
+    }
+
+    @AfterEach
+    public void stop() throws Exception
+    {
+        client.stop();
+        server.stop();
+    }
+
+    @Test
+    public void testTextHandler() throws Exception
+    {
+        TextOnlyHandler handler = new TextOnlyHandler();
+        client.connect(handler, serverUri);
+        assertTrue(handler.openLatch.await(5, TimeUnit.SECONDS));
+        assertTrue(serverSocket.openLatch.await(5, TimeUnit.SECONDS));
+
+        // The server sends a sequence of Binary and Text messages
+        RemoteEndpoint remote = serverSocket.session.getRemote();
+        remote.sendBytes(BufferUtil.toBuffer("this should get rejected"));
+        remote.sendString("WebSocket_Data0");
+        remote.sendString("WebSocket_Data1");
+        serverSocket.session.close(StatusCode.NORMAL, "test complete");
+
+        // The client receives the messages and has discarded the binary message.
+        assertThat(handler.messages.poll(5, TimeUnit.SECONDS), is("WebSocket_Data0"));
+        assertThat(handler.messages.poll(5, TimeUnit.SECONDS), is("WebSocket_Data1"));
+        assertTrue(handler.closeLatch.await(5, TimeUnit.SECONDS));
+        assertThat(handler.closeCode, is(StatusCode.NORMAL));
+        assertThat(handler.closeReason, is("test complete"));
+    }
+
+    @Test
+    public void testBinaryHandler() throws Exception
+    {
+        BinaryOnlyHandler handler = new BinaryOnlyHandler();
+        client.connect(handler, serverUri);
+        assertTrue(handler.openLatch.await(5, TimeUnit.SECONDS));
+        assertTrue(serverSocket.openLatch.await(5, TimeUnit.SECONDS));
+
+        // The server sends a sequence of Binary and Text messages
+        RemoteEndpoint remote = serverSocket.session.getRemote();
+        remote.sendString("this should get rejected");
+        remote.sendBytes(BufferUtil.toBuffer("WebSocket_Data0"));
+        remote.sendBytes(BufferUtil.toBuffer("WebSocket_Data1"));
+        serverSocket.session.close(StatusCode.NORMAL, "test complete");
+
+        // The client receives the messages and has discarded the binary message.
+        assertThat(handler.messages.poll(5, TimeUnit.SECONDS), is(BufferUtil.toBuffer("WebSocket_Data0")));
+        assertThat(handler.messages.poll(5, TimeUnit.SECONDS), is(BufferUtil.toBuffer("WebSocket_Data1")));
+        assertTrue(handler.closeLatch.await(5, TimeUnit.SECONDS));
+        assertThat(handler.closeCode, is(StatusCode.NORMAL));
+        assertThat(handler.closeReason, is("test complete"));
+    }
+
+    @WebSocket
+    public static class TextOnlyHandler extends AbstractHandler
+    {
+        final BlockingArrayQueue<String> messages = new BlockingArrayQueue<>();
+
+        @OnWebSocketMessage
+        public void onMessage(String message)
+        {
+            messages.add(message);
+        }
+    }
+
+    @WebSocket
+    public static class BinaryOnlyHandler extends AbstractHandler
+    {
+        final BlockingArrayQueue<ByteBuffer> messages = new BlockingArrayQueue<>();
+
+        @OnWebSocketMessage
+        public void onMessage(byte[] array, int offset, int length)
+        {
+            messages.add(BufferUtil.toBuffer(array, offset, length));
+        }
+    }
+
+    @WebSocket
+    public static class AbstractHandler
+    {
+        final CountDownLatch openLatch = new CountDownLatch(1);
+        final CountDownLatch closeLatch = new CountDownLatch(1);
+        Session session;
+        int closeCode;
+        String closeReason;
+
+        @OnWebSocketClose
+        public void onClose(int statusCode, String reason)
+        {
+            this.closeCode = statusCode;
+            this.closeReason = reason;
+            this.closeLatch.countDown();
+        }
+
+        @OnWebSocketConnect
+        public void onConnect(Session session)
+        {
+            this.session = session;
+            this.openLatch.countDown();
+        }
+    }
+}