diff --git a/setup.py b/setup.py
index 3f27e12dd..a9315d048 100644
--- a/setup.py
+++ b/setup.py
@@ -96,7 +96,7 @@ def find_meta(meta):
         packages=find_packages(where="src"),
         package_dir={"": "src"},
         install_requires=[
-            "cryptography>=41.0.0,<42",
+            "cryptography>=42.0.0",
         ],
         extras_require={
             "test": ["flaky", "pretend", "pytest>=3.0.1"],
diff --git a/src/OpenSSL/SSL.py b/src/OpenSSL/SSL.py
index a0d0b6acb..013c86dde 100644
--- a/src/OpenSSL/SSL.py
+++ b/src/OpenSSL/SSL.py
@@ -850,7 +850,10 @@ def __init__(self, method):
         self._cookie_generate_helper = None
         self._cookie_verify_helper = None
 
-        self.set_mode(_lib.SSL_MODE_ENABLE_PARTIAL_WRITE)
+        self.set_mode(
+            _lib.SSL_MODE_ENABLE_PARTIAL_WRITE
+            | _lib.SSL_MODE_ACCEPT_MOVING_WRITE_BUFFER
+        )
         if version is not None:
             self.set_min_proto_version(version)
             self.set_max_proto_version(version)
diff --git a/tests/test_crypto.py b/tests/test_crypto.py
index cb2140c3d..cad644c3b 100644
--- a/tests/test_crypto.py
+++ b/tests/test_crypto.py
@@ -1738,7 +1738,7 @@ def test_construction(self):
         certificate = X509()
         assert isinstance(certificate, X509)
         assert type(certificate).__name__ == "X509"
-        assert type(certificate) == X509
+        assert type(certificate) is X509
 
     def test_set_version_wrong_args(self):
         """
@@ -3146,7 +3146,7 @@ def test_construction(self):
         """
         revoked = Revoked()
         assert isinstance(revoked, Revoked)
-        assert type(revoked) == Revoked
+        assert type(revoked) is Revoked
         assert revoked.get_serial() == b"00"
         assert revoked.get_rev_date() is None
         assert revoked.get_reason() is None
@@ -3441,8 +3441,8 @@ def test_get_revoked(self):
 
         revs = crl.get_revoked()
         assert len(revs) == 2
-        assert type(revs[0]) == Revoked
-        assert type(revs[1]) == Revoked
+        assert type(revs[0]) is Revoked
+        assert type(revs[1]) is Revoked
         assert revs[0].get_serial() == b"03AB"
         assert revs[1].get_serial() == b"0100"
         assert revs[0].get_rev_date() == now
diff --git a/tests/test_ssl.py b/tests/test_ssl.py
index 369f6a6d7..32e43d228 100644
--- a/tests/test_ssl.py
+++ b/tests/test_ssl.py
@@ -191,7 +191,7 @@ def join_bytes_or_unicode(prefix, suffix):
     The return type is the same as the type of ``prefix``.
     """
     # If the types are the same, nothing special is necessary.
-    if type(prefix) == type(suffix):
+    if type(prefix) is type(suffix):
         return join(prefix, suffix)
 
     # Otherwise, coerce suffix to the type of prefix.
diff --git a/tox.ini b/tox.ini
index 94d420723..8fe87c86b 100644
--- a/tox.ini
+++ b/tox.ini
@@ -18,7 +18,7 @@ extras =
     test
 deps =
     coverage>=4.2
-    cryptographyMinimum: cryptography==38.0.0
+    cryptographyMinimum: cryptography==41.0.3
     randomorder: pytest-randomly
 setenv =
     # Do not allow the executing environment to pollute the test environment