diff --git a/6d1d17d016.patch b/6d1d17d016.patch
new file mode 100644
index 0000000..8b27ae8
--- /dev/null
+++ b/6d1d17d016.patch
@@ -0,0 +1,34 @@
+From 6d1d17d016d092146b620e4f9338f9b125e33ded Mon Sep 17 00:00:00 2001
+From: Florian Bruhin <me@the-compiler.org>
+Date: Tue, 26 Apr 2022 11:16:27 +0200
+Subject: [PATCH] Adjust imports of deprecated sre_* modules in Python 3.11
+
+Fixes #3309
+See https://github.com/python/cpython/issues/91308
+
+I don't see a way to avoid relying on Python 3.11 internals here, so
+this instead just adjusts the imports to avoid deprecation warnings.
+---
+ .../src/hypothesis/strategies/_internal/regex.py         | 9 +++++++--
+ 1 file changed, 7 insertions(+), 2 deletions(-)
+
+diff --git a/hypothesis-python/src/hypothesis/strategies/_internal/regex.py b/hypothesis-python/src/hypothesis/strategies/_internal/regex.py
+index 5da2b3ba2d..b93e8d192b 100644
+--- a/hypothesis-python/src/hypothesis/strategies/_internal/regex.py
++++ b/hypothesis-python/src/hypothesis/strategies/_internal/regex.py
+@@ -10,8 +10,13 @@
+ 
+ import operator
+ import re
+-import sre_constants as sre
+-import sre_parse
++
++try:  # pragma: no cover
++    import re._constants as sre
++    import re._parser as sre_parse
++except ImportError:  # Python < 3.11
++    import sre_constants as sre  # type: ignore
++    import sre_parse  # type: ignore
+ 
+ from hypothesis import reject, strategies as st
+ from hypothesis.internal.charmap import as_general_categories, categories
diff --git a/a4681f6962.patch b/a4681f6962.patch
new file mode 100644
index 0000000..12f994a
--- /dev/null
+++ b/a4681f6962.patch
@@ -0,0 +1,42 @@
+From a4681f6962ea137db3eec059fb453929eb998fec Mon Sep 17 00:00:00 2001
+From: Zac Hatfield-Dodds <zac.hatfield.dodds@gmail.com>
+Date: Sat, 7 May 2022 23:45:33 -0600
+Subject: [PATCH] Tests work on 3.11.0b1
+
+Thanks to CPython upstream fixes, these tests should now just work
+---
+ hypothesis-python/tests/conftest.py               | 5 -----
+ hypothesis-python/tests/cover/test_lookup_py37.py | 4 ----
+ 2 files changed, 9 deletions(-)
+
+diff --git a/hypothesis-python/tests/conftest.py b/hypothesis-python/tests/conftest.py
+index 988efaf70c..bcbd024903 100644
+--- a/hypothesis-python/tests/conftest.py
++++ b/hypothesis-python/tests/conftest.py
+@@ -37,11 +37,6 @@
+ if sys.version_info >= (3, 11):
+     collect_ignore_glob.append("cover/test_asyncio.py")  # @asyncio.coroutine removed
+ 
+-    assert sys.version_info.releaselevel == "alpha"
+-    # TODO: our traceback elision doesn't work with Python 3.11's nice new format yet
+-    collect_ignore_glob.append("cover/test_traceback_elision.py")
+-    collect_ignore_glob.append("pytest/test_capture.py")
+-
+ 
+ def pytest_configure(config):
+     config.addinivalue_line("markers", "slow: pandas expects this marker to exist.")
+diff --git a/hypothesis-python/tests/cover/test_lookup_py37.py b/hypothesis-python/tests/cover/test_lookup_py37.py
+index bdfbbecd9e..6a1955eb6b 100644
+--- a/hypothesis-python/tests/cover/test_lookup_py37.py
++++ b/hypothesis-python/tests/cover/test_lookup_py37.py
+@@ -163,10 +163,6 @@ def test_resolving_standard_callable_ellipsis(x: collections.abc.Callable[..., E
+     assert isinstance(x(1, 2, 3, a=4, b=5, c=6), Elem)
+ 
+ 
+-@pytest.mark.skipif(
+-    sys.version_info[:3] == (3, 11, 0),
+-    reason="https://github.com/python/cpython/issues/91621",
+-)
+ @given(...)
+ def test_resolving_standard_callable_no_args(x: collections.abc.Callable[[], Elem]):
+     assert isinstance(x, collections.abc.Callable)
diff --git a/python-hypothesis.spec b/python-hypothesis.spec
index 19dceba..ed02c13 100644
--- a/python-hypothesis.spec
+++ b/python-hypothesis.spec
@@ -17,6 +17,10 @@ License:        MPLv2.0
 URL:            https://github.com/HypothesisWorks/hypothesis
 Source0:        %{url}/archive/hypothesis-python-%{version}/hypothesis-%{version}.tar.gz
 
+# Python 3.11 fixes
+Patch:          https://github.com/HypothesisWorks/hypothesis/commit/6d1d17d016.patch
+Patch:          https://github.com/HypothesisWorks/hypothesis/commit/a4681f6962.patch
+
 BuildArch:      noarch
 
 BuildRequires:  python%{python3_pkgversion}-devel