diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 6e23770d..4258fe8b 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -4,6 +4,23 @@ Changelog
 Versions are year-based with a strict backward-compatibility policy.
 The third digit is only for regressions.
 
+24.1.0 (UNRELEASED)
+-------------------
+
+Backward-incompatible changes:
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+- ``pyOpenSSL`` now sets ``SSL_MODE_ACCEPT_MOVING_WRITE_BUFFER`` by default, matching CPython's behavior. `#1287 <https://github.com/pyca/pyopenssl/pull/1287>`_.
+- The minimum ``cryptography`` version is now 42.0.0.
+
+Deprecations:
+^^^^^^^^^^^^^
+
+Changes:
+^^^^^^^^
+
+
+
 24.0.0 (2024-01-22)
 -------------------
 
diff --git a/setup.py b/setup.py
index 2f023168..790d3518 100644
--- a/setup.py
+++ b/setup.py
@@ -93,7 +93,7 @@ def find_meta(meta):
         packages=find_packages(where="src"),
         package_dir={"": "src"},
         install_requires=[
-            "cryptography>=41.0.5,<43",
+            "cryptography>=42.0.0,<43",
         ],
         extras_require={
             "test": ["flaky", "pretend", "pytest>=3.0.1"],
diff --git a/src/OpenSSL/SSL.py b/src/OpenSSL/SSL.py
index 4db5240e..06f38fd2 100644
--- a/src/OpenSSL/SSL.py
+++ b/src/OpenSSL/SSL.py
@@ -163,20 +163,11 @@
 DTLS_SERVER_METHOD = 11
 DTLS_CLIENT_METHOD = 12
 
-try:
-    SSL3_VERSION = _lib.SSL3_VERSION
-    TLS1_VERSION = _lib.TLS1_VERSION
-    TLS1_1_VERSION = _lib.TLS1_1_VERSION
-    TLS1_2_VERSION = _lib.TLS1_2_VERSION
-    TLS1_3_VERSION = _lib.TLS1_3_VERSION
-except AttributeError:
-    # Hardcode constants for cryptography < 3.4, see
-    # https://github.com/pyca/pyopenssl/pull/985#issuecomment-775186682
-    SSL3_VERSION = 768
-    TLS1_VERSION = 769
-    TLS1_1_VERSION = 770
-    TLS1_2_VERSION = 771
-    TLS1_3_VERSION = 772
+SSL3_VERSION = _lib.SSL3_VERSION
+TLS1_VERSION = _lib.TLS1_VERSION
+TLS1_1_VERSION = _lib.TLS1_1_VERSION
+TLS1_2_VERSION = _lib.TLS1_2_VERSION
+TLS1_3_VERSION = _lib.TLS1_3_VERSION
 
 OP_NO_SSLv2 = _lib.SSL_OP_NO_SSLv2
 OP_NO_SSLv3 = _lib.SSL_OP_NO_SSLv3
@@ -864,8 +855,10 @@ def __init__(self, method):
         self._ocsp_data = None
         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/tox.ini b/tox.ini
index d0543d6a..771a0c74 100644
--- a/tox.ini
+++ b/tox.ini
@@ -18,7 +18,7 @@ extras =
     test
 deps =
     coverage>=4.2
-    cryptographyMinimum: cryptography==41.0.5
+    cryptographyMinimum: cryptography==42.0.0
     randomorder: pytest-randomly
 setenv =
     # Do not allow the executing environment to pollute the test environment