diff --git a/packaging/pep517_backend/_backend.py b/packaging/pep517_backend/_backend.py
index f3ea98d3..0fec684f 100644
--- a/packaging/pep517_backend/_backend.py
+++ b/packaging/pep517_backend/_backend.py
@@ -10,7 +10,6 @@
 from shutil import copytree
 from sys import implementation as _system_implementation
 from sys import stderr as _standard_error_stream
-from sys import version_info as _python_version_tuple
 from tempfile import TemporaryDirectory
 from warnings import warn as _warn_that
 
@@ -79,9 +78,6 @@
 PURE_PYTHON_ENV_VAR = 'FROZENLIST_NO_EXTENSIONS'
 """Environment variable name toggle used to opt out of making C-exts."""
 
-IS_PY3_12_PLUS = _python_version_tuple[:2] >= (3, 12)
-"""A flag meaning that the current runtime is Python 3.12 or higher."""
-
 IS_CPYTHON = _system_implementation.name == "cpython"
 """A flag meaning that the current interpreter implementation is CPython."""
 
@@ -343,8 +339,8 @@ def get_requires_for_build_wheel(
         )
 
     c_ext_build_deps = [] if is_pure_python_build else [
-        'Cython >= 3.0.0b3' if IS_PY3_12_PLUS  # Only Cython 3+ is compatible
-        else 'Cython',
+        'Cython ~= 3.0.0; python_version >= "3.12"',
+        'Cython; python_version < "3.12"',
     ]
 
     return _setuptools_get_requires_for_build_wheel(