diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 2a783cd..aae51aa 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -5,6 +5,9 @@ on:
   push:
     branches:
       - master
+  # Run it every month to make sure it still works
+  schedule:
+   - cron:  '0 0 1 * *'
 jobs:
   build:
     name: tests
@@ -16,56 +19,20 @@ jobs:
           - macos-latest
           - windows-latest
         python-version:
-          - "2.7"
-          - "3.0"
-          - "3.1"
-          - "3.2"
-          - "3.3"
-          # coverage (used by pytest-cov) fails to install on 3.4 (setup.py contains an f-string)
-          #- "3.4"
-          - "3.5"
-          - "3.6"
-          - "3.7"
           - "3.8"
           - "3.9"
           - "3.10"
           - "3.11"
-          - "3.12-dev"
+          - "3.12"
+          - "3.13-dev"
           - "pypy2.7"
-          - "pypy3.6"
-          - "pypy3.7"
           - "pypy3.8"
           - "pypy3.9"
-        exclude:
-          # https://foss.heptapod.net/pypy/pypy/-/issues/3314
-          - os: macos-latest
-            python-version: "pypy3.6"
-          # PyPy v3.6 not available on Windows
-          - os: windows-latest
-            python-version: "pypy3.6"
-          # 3.5 and 3.6 no longer available on ubuntu-latest
-          - os: ubuntu-latest
-            python-version: "3.5"
-          - os: ubuntu-latest
-            python-version: "3.6"
-        # Python v3.0-v3.3 can only be installed on Windows
-          - python-version: "3.0"
-          - python-version: "3.1"
-          - python-version: "3.2"
-          - python-version: "3.3"
-        include:
-          - os: windows-latest
-            python-version: "3.0"
-          - os: windows-latest
-            python-version: "3.1"
-          - os: windows-latest
-            python-version: "3.2"
-          - os: windows-latest
-            python-version: "3.3"
+          - "pypy3.10"
       fail-fast: false
     steps:
     - name: Checkout
-      uses: actions/checkout@v3
+      uses: actions/checkout@v4
 
     - name: Set up Python v${{ matrix.python-version }}
       uses: actions/setup-python@v4
diff --git a/README.md b/README.md
index 70cb490..aeab668 100644
--- a/README.md
+++ b/README.md
@@ -7,7 +7,7 @@ bracelogger
 A Python library that enables using the brace-style string formatting in log messages.
 
 Features:
- - Supports a wide range of Python versions (v2.7 - v3.10)
+ - Supports a wide range of Python versions (v2.7 - v3.12)
  - No dependencies
  - Easy to use - no special syntax required
  - Easy to transition to from stdlib logging - just change the `logging.getLogger` calls and message
diff --git a/setup.py b/setup.py
index 3fb3102..f9f8f73 100644
--- a/setup.py
+++ b/setup.py
@@ -40,6 +40,7 @@
         "Programming Language :: Python :: 3.9",
         "Programming Language :: Python :: 3.10",
         "Programming Language :: Python :: 3.11",
+        "Programming Language :: Python :: 3.12",
         "Programming Language :: Python :: Implementation :: CPython",
         "Programming Language :: Python :: Implementation :: PyPy",
         "Intended Audience :: Developers",
diff --git a/tests/test_bracelogger.py b/tests/test_bracelogger.py
index 2998908..c846077 100644
--- a/tests/test_bracelogger.py
+++ b/tests/test_bracelogger.py
@@ -1,6 +1,7 @@
 #!/usr/bin/env python
 
 import logging
+import sys
 
 import bracelogger
 
@@ -96,6 +97,9 @@ def test_all_levels(caplog):
     """Test logging at all documented levels"""
 
     LEVELS = ("debug", "info", "warn", "warning", "error", "exception", "critical", "fatal")
+    if sys.version_info >= (3, 13):
+        LEVELS.remove("warn")  # has been deprecated since 3.1, finally removed in v3.13
+
     TEMPLATE = "This is a {}-level log"
 
     caplog.set_level(1)  # capture everything