diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 6a164b62..5dfd4a35 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -1,6 +1,10 @@
 Changes
 =======
 
+4.0.3
+~~~~
+* FIX: Stop requiring bleeding-edge Cython unless necesasry (for Python 3.12).  #206
+
 4.0.2
 ~~~~~
 * FIX: AttributeError on certain methods. #191
diff --git a/README.rst b/README.rst
index e3cb98cf..f35fbaaa 100644
--- a/README.rst
+++ b/README.rst
@@ -54,7 +54,7 @@ To check out the development sources, you can use Git_::
 You may also download source tarballs of any snapshot from that URL.
 
 Source releases will require a C compiler in order to build `line_profiler`.
-In addition, git checkouts will also require Cython_ >= 0.10. Source releases
+In addition, git checkouts will also require Cython. Source releases
 on PyPI should contain the pregenerated C sources, so Cython should not be
 required in that case.
 
@@ -381,8 +381,7 @@ Frequently Asked Questions
     It should contain the generated C sources already. If you are running into
     problems, that may be a bug; let me know. If you are building from
     a git checkout or snapshot, you will need Cython to generate the
-    C sources. You will probably need version 0.10 or higher. There is a bug in
-    some earlier versions in how it handles NULL PyObject* pointers.
+    C sources.
 
     As of version ``3.0.0`` manylinux wheels containing the binaries are
     available on pypi. Work is still needed to publish osx and win32 wheels.
diff --git a/kernprof.py b/kernprof.py
index b3a7d619..54cb8c2d 100755
--- a/kernprof.py
+++ b/kernprof.py
@@ -13,7 +13,7 @@
 
 # NOTE: This version needs to be manually maintained with the line_profiler
 # __version__ for now.
-__version__ = '4.0.2'
+__version__ = '4.0.3'
 
 # Guard the import of cProfile such that 3.x people
 # without lsprof can still use this script.
diff --git a/line_profiler/line_profiler.py b/line_profiler/line_profiler.py
index e9cf56ad..bfcd009e 100755
--- a/line_profiler/line_profiler.py
+++ b/line_profiler/line_profiler.py
@@ -16,7 +16,7 @@
         f'Has it been compiled? Underlying error is ex={ex!r}'
     )
 
-__version__ = '4.0.2'
+__version__ = '4.0.3'
 
 
 def load_ipython_extension(ip):
diff --git a/pyproject.toml b/pyproject.toml
index 4eb4fdd2..46ce0180 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,5 +1,9 @@
 [build-system]
-requires = ["setuptools>=41.0.1", "Cython>=3.0.0a11"]
+requires = [
+    "setuptools>=41.0.1",
+    "Cython==3.0.0a11            ; python_version < '4.0'  and python_version >= '3.12' ",
+    "Cython>=0.29.24,<=3.0.0a11  ; python_version < '3.12' ",
+]
 build-backend = "setuptools.build_meta"  # comment out to disable pep517
 
 [tool.coverage.run]
diff --git a/requirements/build.txt b/requirements/build.txt
index 6a282aec..94ad12ea 100644
--- a/requirements/build.txt
+++ b/requirements/build.txt
@@ -1,5 +1,7 @@
 # Cython is the only hard requirement
-Cython>=3.0.0a11
+Cython==3.0.0a11             ; python_version < '4.0'  and python_version >= '3.12'    # Python 3.12+
+Cython>=0.29.24,<=3.0.0a11   ; python_version < '3.12'                                 # Python 3.6 - 3.11
+
 scikit-build>=0.11.1
 cmake>=3.21.2
 ninja>=1.10.2