diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 4c060ea1c1e..29d4b4083da 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -1843,11 +1843,14 @@ if _have_threads:
                         self.sock, server_side=True)
                     self.server.selected_npn_protocols.append(self.sslconn.selected_npn_protocol())
                     self.server.selected_alpn_protocols.append(self.sslconn.selected_alpn_protocol())
-                except (ssl.SSLError, ConnectionResetError) as e:
+                except (ssl.SSLError, ConnectionResetError, OSError) as e:
                     # We treat ConnectionResetError as though it were an
                     # SSLError - OpenSSL on Ubuntu abruptly closes the
                     # connection when asked to use an unsupported protocol.
                     #
+                    # OSError may occur with wrong protocols, e.g. both
+                    # sides use PROTOCOL_TLS_SERVER.
+                    #
                     # XXX Various errors can have happened here, for example
                     # a mismatching protocol version, an invalid certificate,
                     # or a low-level bug. This should be made more discriminating.
diff --git a/Misc/NEWS.d/next/Tests/2017-09-05-14-23-35.bpo-31320.JRDHx7.rst b/Misc/NEWS.d/next/Tests/2017-09-05-14-23-35.bpo-31320.JRDHx7.rst
new file mode 100644
index 00000000000..8b7163dfe79
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2017-09-05-14-23-35.bpo-31320.JRDHx7.rst
@@ -0,0 +1 @@
+Silence traceback in test_ssl