diff --git a/doc/api/ssl.rst b/doc/api/ssl.rst
index c678b2807..ffa2d1b5a 100644
--- a/doc/api/ssl.rst
+++ b/doc/api/ssl.rst
@@ -27,7 +27,7 @@ Context, Connection.
              VERIFY_PEER
              VERIFY_FAIL_IF_NO_PEER_CERT
 
-    These constants represent the verification mode used by the Context
+    These constants represent the verification mode used by the Context and Connection
     object's :py:meth:`set_verify` method.
 
 
diff --git a/src/OpenSSL/SSL.py b/src/OpenSSL/SSL.py
index 506354d9c..91804a472 100644
--- a/src/OpenSSL/SSL.py
+++ b/src/OpenSSL/SSL.py
@@ -1562,6 +1562,8 @@ def __init__(self, context, socket=None):
         _lib.SSL_set_mode(self._ssl, _lib.SSL_MODE_AUTO_RETRY)
         self._context = context
         self._app_data = None
+        self._verify_helper = None
+        self._verify_callback = None
 
         # References to strings used for Next Protocol Negotiation. OpenSSL's
         # header files suggest that these might get copied at some point, but
@@ -1609,6 +1611,8 @@ def __getattr__(self, name):
             return getattr(self._socket, name)
 
     def _raise_ssl_error(self, ssl, result):
+        if self._verify_helper is not None:
+            self._verify_helper.raise_if_problem()
         if self._context._verify_helper is not None:
             self._context._verify_helper.raise_if_problem()
         if self._context._npn_advertise_helper is not None:
@@ -2497,6 +2501,70 @@ def request_ocsp(self):
         )
         _openssl_assert(rc == 1)
 
+    def set_verify(self, mode, callback):
+        """
+        Set the verification flags for this Connection object to *mode* and specify
+        that *callback* should be used for verification callbacks.
+
+        While a Connection will inherit the verification config from its Context,
+        it is also possible to change it once the Connection has been instantiated
+        already.
+
+        :param mode: The verify mode, this should be one of
+            :const:`VERIFY_NONE` and :const:`VERIFY_PEER`. If
+            :const:`VERIFY_PEER` is used, *mode* can be OR:ed with
+            :const:`VERIFY_FAIL_IF_NO_PEER_CERT` and
+            :const:`VERIFY_CLIENT_ONCE` to further control the behaviour.
+        :param callback: The Python callback to use.  This should take five
+            arguments: A Connection object, an X509 object, and three integer
+            variables, which are in turn potential error number, error depth
+            and return code. *callback* should return True if verification
+            passes and False otherwise.
+        :return: None
+
+        See SSL_set_verify(3SSL) for further details.
+        """
+        if not isinstance(mode, integer_types):
+            raise TypeError("mode must be an integer")
+
+        if not callable(callback):
+            raise TypeError("callback must be callable")
+
+        self._verify_helper = _VerifyHelper(callback)
+        self._verify_callback = self._verify_helper.callback
+        _lib.SSL_set_verify(self._ssl, mode, self._verify_callback)
+
+    def set_verify_depth(self, depth):
+        """
+        Set the maximum depth for the certificate chain verification that shall
+        be allowed for this Connection object.
+
+        :param depth: An integer specifying the verify depth
+        :return: None
+        """
+        if not isinstance(depth, integer_types):
+            raise TypeError("depth must be an integer")
+
+        _lib.SSL_set_verify_depth(self._ssl, depth)
+
+    def get_verify_mode(self):
+        """
+        Retrieve the Connection object's verify mode, as set by
+        :meth:`set_verify`.
+
+        :return: The verify mode
+        """
+        return _lib.SSL_get_verify_mode(self._ssl)
+
+    def get_verify_depth(self):
+        """
+        Retrieve the Connection object's verify depth, as set by
+        :meth:`set_verify_depth`.
+
+        :return: The verify depth
+        """
+        return _lib.SSL_get_verify_depth(self._ssl)
+
 
 # This is similar to the initialization calls at the end of OpenSSL/crypto.py
 # but is exercised mostly by the Context initializer.
diff --git a/tests/test_ssl.py b/tests/test_ssl.py
index 7916d435d..59056edbe 100644
--- a/tests/test_ssl.py
+++ b/tests/test_ssl.py
@@ -798,6 +798,17 @@ def test_verify_depth(self):
         context.set_verify_depth(11)
         assert context.get_verify_depth() == 11
 
+    def test_connection_verify_depth(self):
+        """
+        `Connection.set_verify_depth` sets the number of certificates in
+        a chain to follow before giving up.  The value can be retrieved with
+        `Connection.get_verify_depth`.
+        """
+        context = Context(TLSv1_METHOD)
+        connection = Connection(context, None)
+        connection.set_verify_depth(11)
+        assert connection.get_verify_depth() == 11
+
     def _write_encrypted_pem(self, passphrase, tmpfile):
         """
         Write a new private key out to a new file, encrypted using the given
@@ -1285,6 +1296,33 @@ def verify_callback(*args):
 
         assert "silly verify failure" == str(exc.value)
 
+    def test_set_verify_callback_in_connection_object(self):
+        """
+        The first argument passed to the verify callback is the
+        `Connection` instance for which verification is taking place.
+        """
+        serverContext = Context(TLSv1_METHOD)
+        serverContext.use_privatekey(
+            load_privatekey(FILETYPE_PEM, cleartextPrivateKeyPEM))
+        serverContext.use_certificate(
+            load_certificate(FILETYPE_PEM, cleartextCertificatePEM))
+        serverConnection = Connection(serverContext, None)
+
+        class VerifyCallback(object):
+            def callback(self, connection, *args):
+                self.connection = connection
+                return 1
+
+        verify = VerifyCallback()
+        clientContext = Context(TLSv1_METHOD)
+        clientConnection = Connection(clientContext, None)
+        clientConnection.set_verify(VERIFY_PEER, verify.callback)
+        clientConnection.set_connect_state()
+
+        handshake_in_memory(clientConnection, serverConnection)
+
+        assert verify.connection is clientConnection
+
     def test_add_extra_chain_cert(self, tmpdir):
         """
         `Context.add_extra_chain_cert` accepts an `X509`
@@ -1418,6 +1456,18 @@ def test_set_verify_mode(self):
             VERIFY_PEER | VERIFY_CLIENT_ONCE, lambda *args: None)
         assert context.get_verify_mode() == (VERIFY_PEER | VERIFY_CLIENT_ONCE)
 
+    def test_connection_get_verify_mode(self):
+        """
+        `Connection.get_verify_mode` returns the verify mode flags previously
+        passed to `Connection.set_verify`.
+        """
+        context = Context(TLSv1_METHOD)
+        connection = Connection(context, None)
+        assert connection.get_verify_mode() == 0
+        connection.set_verify(
+            VERIFY_PEER | VERIFY_CLIENT_ONCE, lambda *args: None)
+        assert connection.get_verify_mode() == (VERIFY_PEER | VERIFY_CLIENT_ONCE)
+
     @pytest.mark.parametrize('mode', [None, 1.0, object(), 'mode'])
     def test_set_verify_wrong_mode_arg(self, mode):
         """