diff --git a/.travis.yml b/.travis.yml
index 8c22b32..8746ea4 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,11 +2,13 @@ language: python
 
 python:
   - 2.7
+  - 3.5
   - 3.6
   - 3.7
   - 3.8
   - 3.9
 
+
 before_install:
   - sudo apt-get install python-dev libevent-dev
   - pip install Cython
diff --git a/test/test_websocket.py b/test/test_websocket.py
index 42ec208..29e451f 100644
--- a/test/test_websocket.py
+++ b/test/test_websocket.py
@@ -5,10 +5,13 @@
 import struct
 
 try:
+    from io import BytesIO
     from unittest.mock import MagicMock, call, patch
 except ImportError:
+    from StringIO import StringIO as BytesIO
     from mock import MagicMock, call, patch
 
+
 from ws4py.framing import Frame, \
      OPCODE_CONTINUATION, OPCODE_TEXT, \
      OPCODE_BINARY, OPCODE_CLOSE, OPCODE_PING, OPCODE_PONG
@@ -180,6 +183,25 @@ def test_sending_ping(self):
         ws.ping("hello")
         m.sendall.assert_called_once_with(tm)
 
+    def test_spill_frame(self):
+        data = b"hello"
+        buf = BytesIO(data + b"spillover")
+
+        sock = MagicMock()
+        sock._ssl = object()  # for WebSocket._is_secure logic
+        sock.recv.side_effect = buf.read
+        sock.pending.side_effect = lambda: buf.tell() < len(buf.getvalue())
+
+        ws = WebSocket(sock=sock)
+        ws.stream = MagicMock()
+
+        self.assertTrue(ws._is_secure)
+
+        ws.reading_buffer_size = len(data)
+        ws.once()
+
+        ws.stream.parser.send.assert_called_once_with(data)
+
 
     @patch("ws4py.websocket.Heartbeat")
     def test_run(self, mocker):