diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index b27ad002c..942261e04 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -20,6 +20,9 @@ Deprecations:
 Changes:
 ^^^^^^^^
 
+- Add ``OpenSSL.SSL.Connection.set_verify`` and ``OpenSSL.SSL.Connection.get_verify_mode``
+  to override the context object's verification flags.
+  `#1073 <https://github.com/pyca/pyopenssl/pull/1073>`_
 - Expose wrappers for some `DTLS
   <https://en.wikipedia.org/wiki/Datagram_Transport_Layer_Security>`_
   primitives. `#1026 <https://github.com/pyca/pyopenssl/pull/1026>`_
diff --git a/setup.py b/setup.py
index ecc23cca3..9d611680d 100755
--- a/setup.py
+++ b/setup.py
@@ -93,7 +93,7 @@ def find_meta(meta):
         package_dir={"": "src"},
         install_requires=[
             # Fix cryptographyMinimum in tox.ini when changing this!
-            "cryptography>=35.0",
+            "cryptography>=37.0",
         ],
         extras_require={
             "test": ["flaky", "pretend", "pytest>=3.0.1"],
diff --git a/src/OpenSSL/SSL.py b/src/OpenSSL/SSL.py
index 12374b707..0f721dfc3 100644
--- a/src/OpenSSL/SSL.py
+++ b/src/OpenSSL/SSL.py
@@ -1736,6 +1736,35 @@ def get_servername(self):
 
         return _ffi.string(name)
 
+    def set_verify(self, mode, callback=None):
+        """
+        Override the Context object's verification flags for this specific
+        connection. See :py:meth:`Context.set_verify` for details.
+        """
+        if not isinstance(mode, int):
+            raise TypeError("mode must be an integer")
+
+        if callback is None:
+            self._verify_helper = None
+            self._verify_callback = None
+            _lib.SSL_set_verify(self._ssl, mode, _ffi.NULL)
+        else:
+            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 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 set_ciphertext_mtu(self, mtu):
         """
         For DTLS, set the maximum UDP payload size (*not* including IP/UDP
diff --git a/tests/test_ssl.py b/tests/test_ssl.py
index ccc8a3870..7d5ed5112 100644
--- a/tests/test_ssl.py
+++ b/tests/test_ssl.py
@@ -2629,6 +2629,51 @@ def test_get_verified_chain_unconnected(self):
         server = Connection(ctx, None)
         assert None is server.get_verified_chain()
 
+    def test_set_verify_overrides_context(self):
+        context = Context(SSLv23_METHOD)
+        context.set_verify(VERIFY_PEER)
+        conn = Connection(context, None)
+        conn.set_verify(VERIFY_NONE)
+
+        assert context.get_verify_mode() == VERIFY_PEER
+        assert conn.get_verify_mode() == VERIFY_NONE
+
+        with pytest.raises(TypeError):
+            conn.set_verify(None)
+
+        with pytest.raises(TypeError):
+            conn.set_verify(VERIFY_PEER, "not a callable")
+
+    def test_set_verify_callback_reference(self):
+        """
+        The callback for certificate verification should only be forgotten if the context and all connections
+        created by it do not use it anymore.
+        """
+        def callback(conn, cert, errnum, depth, ok):  # pragma: no cover
+            return ok
+
+        tracker = ref(callback)
+
+        context = Context(SSLv23_METHOD)
+        context.set_verify(VERIFY_PEER, callback)
+        del callback
+
+        conn = Connection(context, None)
+        context.set_verify(VERIFY_NONE)
+
+        collect()
+        collect()
+        assert tracker()
+
+        conn.set_verify(VERIFY_PEER, lambda conn, cert, errnum, depth, ok: ok)
+        collect()
+        collect()
+        callback = tracker()
+        if callback is not None:
+            referrers = get_referrers(callback)
+            if len(referrers) > 1:  # pragma: nocover
+                pytest.fail("Some references remain: %r" % (referrers,))
+
     def test_get_session_unconnected(self):
         """
         `Connection.get_session` returns `None` when used with an object
diff --git a/tox.ini b/tox.ini
index 5883e7ade..8edf55d31 100644
--- a/tox.ini
+++ b/tox.ini
@@ -10,7 +10,7 @@ extras =
 deps =
     coverage>=4.2
     cryptographyMain: git+https://github.com/pyca/cryptography.git
-    cryptographyMinimum: cryptography==35.0
+    cryptographyMinimum: cryptography==37.0
     randomorder: pytest-randomly
 setenv =
     # Do not allow the executing environment to pollute the test environment