diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index ab5a2bc..1c8005e 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -26,9 +26,10 @@ jobs:
           - "3.9"
           - "3.10"
           - "3.11"
-          # CPython 3.12 final is scheduled for October 2023:
-          # https://peps.python.org/pep-0693/
           - "3.12"
+          # CPython 3.13 final is scheduled for October 2024:
+          # https://peps.python.org/pep-0719/
+          - "3.13"
           # Python 2.7 was removed from GHA setup-python in June 2023:
           # https://github.com/actions/setup-python/issues/672
 
@@ -55,13 +56,15 @@ jobs:
           - os: windows-latest
             python: 3.6
           - os: windows-latest
-            python: 3.11
+            python: 3.12
 
           # macOS: test old and new Python
           - os: macos-latest
             python: 3.6
           - os: macos-latest
-            python: 3.11
+            python: 3.12
+
+          # Ubuntu: test deadsnakes Python not supported by GHA python-versions
           - os: ubuntu-20.04
             python: 3.5
           - os: ubuntu-20.04
diff --git a/.readthedocs.yaml b/.readthedocs.yaml
index de85e78..735b67d 100644
--- a/.readthedocs.yaml
+++ b/.readthedocs.yaml
@@ -6,7 +6,7 @@ version: 2
 build:
   os: ubuntu-22.04
   tools:
-    python: "3.11"
+    python: "3.12"
 
 sphinx:
    configuration: docs/conf.py
diff --git a/docs/api.rst b/docs/api.rst
index 3725b4e..d4846db 100644
--- a/docs/api.rst
+++ b/docs/api.rst
@@ -7,7 +7,7 @@ functions for old Python versions.
 
 Supported Python versions:
 
-* Python 3.5 - 3.11
+* Python 3.5 - 3.12
 * PyPy 2.7
 * PyPy 3.6 - 3.9
 
diff --git a/runtests.py b/runtests.py
index 38507a1..28b2982 100755
--- a/runtests.py
+++ b/runtests.py
@@ -41,6 +41,7 @@
     "python3.10",
     "python3.11",
     "python3.12",
+    "python3.13",
     "pypy",
     "pypy2",
     "pypy2.7",
diff --git a/tests/setup.py b/tests/setup.py
index 4deaa36..2e10c15 100755
--- a/tests/setup.py
+++ b/tests/setup.py
@@ -14,10 +14,6 @@
 
 # C++ is only supported on Python 3.6 and newer
 TEST_CPP = (sys.version_info >= (3, 6))
-if 0x30b0000 <= sys.hexversion <= 0x30b00b3:
-    # Don't test C++ on Python 3.11b1 - 3.11b3: these versions have C++
-    # compatibility issues.
-    TEST_CPP = False
 
 SRC_DIR = os.path.normpath(os.path.join(os.path.dirname(__file__), '..'))