diff --git a/0001-Patch-out-maximum-Python-version-check.patch b/0001-Patch-out-maximum-Python-version-check.patch
deleted file mode 100644
index bd5f1fe..0000000
--- a/0001-Patch-out-maximum-Python-version-check.patch
+++ /dev/null
@@ -1,27 +0,0 @@
-From 6e526cacbd163f10db5cda62e10744f31d2cb5ad Mon Sep 17 00:00:00 2001
-From: "Benjamin A. Beasley" <code@musicinmybrain.net>
-Date: Tue, 7 Mar 2023 10:47:38 -0500
-Subject: [PATCH] Patch out maximum Python version check
-
-Fedora must build this package with the current version of Python,
-whether upstream is ready or not.
----
- setup.py | 2 +-
- 1 file changed, 1 insertion(+), 1 deletion(-)
-
-diff --git a/setup.py b/setup.py
-index 02b1604..b08653d 100644
---- a/setup.py
-+++ b/setup.py
-@@ -46,7 +46,7 @@ def _guard_py_ver():
-     max_py = parse(max_python_version)
-     cur_py = parse('.'.join(map(str, sys.version_info[:3])))
- 
--    if not min_py <= cur_py < max_py:
-+    if not min_py <= cur_py:
-         msg = ('Cannot install on Python version {}; only versions >={},<{} '
-                'are supported.')
-         raise RuntimeError(msg.format(cur_py, min_py, max_py))
--- 
-2.39.2
-
diff --git a/0001-Remove-maximum-Python-version-limit.patch b/0001-Remove-maximum-Python-version-limit.patch
new file mode 100644
index 0000000..ff18e9f
--- /dev/null
+++ b/0001-Remove-maximum-Python-version-limit.patch
@@ -0,0 +1,58 @@
+From 4ad14e2911329832c3fa9025a2fadc921f5bedd8 Mon Sep 17 00:00:00 2001
+From: Andre Masella <andre@masella.name>
+Date: Tue, 14 Mar 2023 14:55:40 -0400
+Subject: [PATCH] Remove maximum Python version limit
+
+Allow any new version of Python for llvmlite. Closes #912
+---
+ azure-pipelines.yml | 4 ++++
+ setup.py            | 8 +++-----
+ 2 files changed, 7 insertions(+), 5 deletions(-)
+
+diff --git a/azure-pipelines.yml b/azure-pipelines.yml
+index 0b14f97..759187a 100644
+--- a/azure-pipelines.yml
++++ b/azure-pipelines.yml
+@@ -38,6 +38,10 @@ jobs:
+         PYTHON: '3.10'
+         CONDA_ENV: cienv
+         RUN_FLAKE8: yes
++      py311:
++        PYTHON: '3.11'
++        CONDA_ENV: cienv
++        RUN_FLAKE8: yes
+         RUN_CLANG_FORMAT: yes
+ # temporarily disabled
+ #       pypy:
+diff --git a/setup.py b/setup.py
+index 02b1604..2a546e6 100644
+--- a/setup.py
++++ b/setup.py
+@@ -33,7 +33,6 @@ except ImportError:
+ 
+ 
+ min_python_version = "3.7"
+-max_python_version = "3.11"  # exclusive
+ 
+ 
+ def _guard_py_ver():
+@@ -43,13 +42,12 @@ def _guard_py_ver():
+     parse = _version_module.parse
+ 
+     min_py = parse(min_python_version)
+-    max_py = parse(max_python_version)
+     cur_py = parse('.'.join(map(str, sys.version_info[:3])))
+ 
+-    if not min_py <= cur_py < max_py:
+-        msg = ('Cannot install on Python version {}; only versions >={},<{} '
++    if not min_py <= cur_py:
++        msg = ('Cannot install on Python version {}; only versions >={} '
+                'are supported.')
+-        raise RuntimeError(msg.format(cur_py, min_py, max_py))
++        raise RuntimeError(msg.format(cur_py, min_py))
+ 
+ 
+ _guard_py_ver()
+-- 
+2.39.2
+
diff --git a/python-llvmlite.spec b/python-llvmlite.spec
index d5426d4..52be545 100644
--- a/python-llvmlite.spec
+++ b/python-llvmlite.spec
@@ -33,18 +33,19 @@ License:        BSD-2-Clause AND LicenseRef-Fedora-Public-Domain
 URL:            http://llvmlite.pydata.org/
 Source0:        %{forgesource}
 
-# Patch out maximum Python version check
+# Backport upstream commit:
+#   Remove maximum Python version limit
 #
-# Fedora must build this package with the current version of Python,
-# whether upstream is ready or not.
-#
-# Feature request / discussion issue for doing this without a patch:
+#   Allow any new version of Python for llvmlite. Closes #912
+#   https://github.com/numba/llvmlite/commit/9ea5668fff6d0e4099d7907aafae40df5b4c8655
+# Fixes:
 #   “Escape hatch” for maximum Python version check
 #   https://github.com/numba/llvmlite/issues/912
 # See also:
 #   python 3.10 support
 #   https://github.com/numba/llvmlite/issues/740
-Patch:          0001-Patch-out-maximum-Python-version-check.patch
+# To be released in 0.40.0 and 0.41.0. Cherry-picked onto tag v0.39.1:
+Patch:          0001-Remove-maximum-Python-version-limit.patch
 
 BuildRequires:  pyproject-rpm-macros
 BuildRequires:  python3-devel