diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 7a3d9f8..cf4c17f 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -96,23 +96,24 @@ jobs:
       fail-fast: false
       matrix:
         python-version:
-          - "pypy-3.9"
+          - "pypy-3.10"
           - "3.7"
           - "3.8"
           - "3.9"
           - "3.10"
           - "3.11"
           - "3.12"
+          - "3.13.0-alpha - 3.13.0"
         os: [ubuntu-20.04, macos-11]
         exclude:
           - os: macos-11
-            python-version: "pypy-3.9"
+            python-version: "pypy-3.10"
 
     steps:
       - name: checkout
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
       - name: Set up Python ${{ matrix.python-version }}
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python-version }}
       ###
@@ -134,7 +135,18 @@ jobs:
           restore-keys: |
             ${{ runner.os }}-pip-
 
+      - name: Install Build Dependencies (3.13.0-alpha - 3.13.0)
+        if: matrix.python-version == '3.13.0-alpha - 3.13.0'
+        run: |
+          pip install -U pip
+          pip install -U setuptools wheel twine
+          # cffi will probably have no public release until a Python 3.13 beta
+          # or even RC release, see https://github.com/python-cffi/cffi/issues/23
+          pip install -U "cffi @ https://github.com/python-cffi/cffi/archive/refs/heads/main.zip"
+          # twine has no release for 3.13, yet, see https://github.com/pypa/twine/issues/1030
+          pip install -U "git+https://github.com/pypa/twine.git#egg=twine"
       - name: Install Build Dependencies
+        if: matrix.python-version != '3.13.0-alpha - 3.13.0'
         run: |
           pip install -U pip
           pip install -U setuptools wheel twine cffi
@@ -178,7 +190,15 @@ jobs:
           python setup.py build_ext -i
           python setup.py bdist_wheel
 
+      - name: Install zope.index and dependencies (3.13.0-alpha - 3.13.0)
+        if: matrix.python-version == '3.13.0-alpha - 3.13.0'
+        run: |
+          # Install to collect dependencies into the (pip) cache.
+          # Use "--pre" here because dependencies with support for this future
+          # Python release may only be available as pre-releases
+          pip install --pre .[test]
       - name: Install zope.index and dependencies
+        if: matrix.python-version != '3.13.0-alpha - 3.13.0'
         run: |
           # Install to collect dependencies into the (pip) cache.
           pip install .[test]
@@ -190,7 +210,7 @@ jobs:
       - name: Upload zope.index wheel (macOS x86_64)
         if: >
           startsWith(runner.os, 'Mac')
-        uses: actions/upload-artifact@v3
+        uses: actions/upload-artifact@v4
         with:
           name: zope.index-${{ runner.os }}-${{ matrix.python-version }}.whl
           path: dist/*x86_64.whl
@@ -199,7 +219,7 @@ jobs:
           startsWith(runner.os, 'Mac')
           && !(startsWith(matrix.python-version, 'pypy')
                || matrix.python-version == '3.7')
-        uses: actions/upload-artifact@v3
+        uses: actions/upload-artifact@v4
         with:
           # The arm64 wheel is uploaded with a different name just so it can be
           # manually downloaded when desired. The wheel itself *cannot* be tested
@@ -209,7 +229,7 @@ jobs:
       - name: Upload zope.index wheel (all other platforms)
         if: >
           !startsWith(runner.os, 'Mac')
-        uses: actions/upload-artifact@v3
+        uses: actions/upload-artifact@v4
         with:
           name: zope.index-${{ runner.os }}-${{ matrix.python-version }}.whl
           path: dist/*whl
@@ -222,6 +242,7 @@ jobs:
           && startsWith(github.ref, 'refs/tags')
           && startsWith(runner.os, 'Mac')
           && !startsWith(matrix.python-version, 'pypy')
+          && !startsWith(matrix.python-version, '3.13.0-alpha - 3.13.0')
         env:
           TWINE_PASSWORD: ${{ secrets.TWINE_PASSWORD }}
         run: |
@@ -234,23 +255,24 @@ jobs:
       fail-fast: false
       matrix:
         python-version:
-          - "pypy-3.9"
+          - "pypy-3.10"
           - "3.7"
           - "3.8"
           - "3.9"
           - "3.10"
           - "3.11"
           - "3.12"
+          - "3.13.0-alpha - 3.13.0"
         os: [ubuntu-20.04, macos-11]
         exclude:
           - os: macos-11
-            python-version: "pypy-3.9"
+            python-version: "pypy-3.10"
 
     steps:
       - name: checkout
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
       - name: Set up Python ${{ matrix.python-version }}
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python-version }}
       ###
@@ -273,11 +295,29 @@ jobs:
             ${{ runner.os }}-pip-
 
       - name: Download zope.index wheel
-        uses: actions/download-artifact@v3
+        uses: actions/download-artifact@v4
         with:
           name: zope.index-${{ runner.os }}-${{ matrix.python-version }}.whl
           path: dist/
+      - name: Install zope.index 3.13.0-alpha - 3.13.0
+        if: ${{ startsWith(matrix.python-version, '3.13.0-alpha - 3.13.0') }}
+        run: |
+          pip install -U wheel setuptools
+          # cffi will probably have no public release until a beta or even RC
+          # version of Python 3.13, see https://github.com/python-cffi/cffi/issues/23
+          pip install -U 'cffi @ https://github.com/python-cffi/cffi/archive/refs/heads/main.zip ; platform_python_implementation == "CPython"'
+          # coverage has a wheel on PyPI for a future python version which is
+          # not ABI compatible with the current one, so build it from sdist:
+          pip install -U --no-binary :all: coverage
+          # Unzip into src/ so that testrunner can find the .so files
+          # when we ask it to load tests from that directory. This
+          # might also save some build time?
+          unzip -n dist/zope.index-*whl -d src
+          # Use "--pre" here because dependencies with support for this future
+          # Python release may only be available as pre-releases
+          pip install --pre -U -e .[test]
       - name: Install zope.index
+        if: ${{ !startsWith(matrix.python-version, '3.13.0-alpha - 3.13.0') }}
         run: |
           pip install -U wheel setuptools
           pip install -U coverage
@@ -325,9 +365,9 @@ jobs:
 
     steps:
       - name: checkout
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
       - name: Set up Python ${{ matrix.python-version }}
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python-version }}
       ###
@@ -350,7 +390,7 @@ jobs:
             ${{ runner.os }}-pip-
 
       - name: Download zope.index wheel
-        uses: actions/download-artifact@v3
+        uses: actions/download-artifact@v4
         with:
           name: zope.index-${{ runner.os }}-${{ matrix.python-version }}.whl
           path: dist/
@@ -376,9 +416,9 @@ jobs:
 
     steps:
       - name: checkout
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
       - name: Set up Python ${{ matrix.python-version }}
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python-version }}
       ###
@@ -401,7 +441,7 @@ jobs:
             ${{ runner.os }}-pip-
 
       - name: Download zope.index wheel
-        uses: actions/download-artifact@v3
+        uses: actions/download-artifact@v4
         with:
           name: zope.index-${{ runner.os }}-${{ matrix.python-version }}.whl
           path: dist/
@@ -429,9 +469,9 @@ jobs:
 
     steps:
       - name: checkout
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
       - name: Set up Python ${{ matrix.python-version }}
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python-version }}
       ###
@@ -481,7 +521,7 @@ jobs:
           bash .manylinux.sh
 
       - name: Upload zope.index wheels
-        uses: actions/upload-artifact@v3
+        uses: actions/upload-artifact@v4
         with:
           path: wheelhouse/*whl
           name: manylinux_${{ matrix.image }}_wheels.zip
diff --git a/.manylinux-install.sh b/.manylinux-install.sh
index 614917e..725b49c 100755
--- a/.manylinux-install.sh
+++ b/.manylinux-install.sh
@@ -28,6 +28,7 @@ yum -y install libffi-devel
 
 tox_env_map() {
     case $1 in
+        *"cp313"*) echo 'py313';;
         *"cp37"*) echo 'py37';;
         *"cp38"*) echo 'py38';;
         *"cp39"*) echo 'py39';;
@@ -41,14 +42,20 @@ tox_env_map() {
 # Compile wheels
 for PYBIN in /opt/python/*/bin; do
     if \
+       [[ "${PYBIN}" == *"cp313"* ]] || \
        [[ "${PYBIN}" == *"cp311"* ]] || \
        [[ "${PYBIN}" == *"cp312"* ]] || \
        [[ "${PYBIN}" == *"cp37"* ]] || \
        [[ "${PYBIN}" == *"cp38"* ]] || \
        [[ "${PYBIN}" == *"cp39"* ]] || \
        [[ "${PYBIN}" == *"cp310"* ]] ; then
-        "${PYBIN}/pip" install -e /io/
-        "${PYBIN}/pip" wheel /io/ -w wheelhouse/
+        if [[ "${PYBIN}" == *"cp313"* ]] ; then
+            "${PYBIN}/pip" install --pre -e /io/
+            "${PYBIN}/pip" wheel /io/ --pre -w wheelhouse/
+        else
+            "${PYBIN}/pip" install -e /io/
+            "${PYBIN}/pip" wheel /io/ -w wheelhouse/
+        fi
         if [ `uname -m` == 'aarch64' ]; then
           cd /io/
           ${PYBIN}/pip install tox
diff --git a/.meta.toml b/.meta.toml
index e38f0ab..500ad3d 100644
--- a/.meta.toml
+++ b/.meta.toml
@@ -2,7 +2,7 @@
 # https://github.com/zopefoundation/meta/tree/master/config/c-code
 [meta]
 template = "c-code"
-commit-id = "978a8a28"
+commit-id = "e45966cd"
 
 [python]
 with-appveyor = true
diff --git a/CHANGES.rst b/CHANGES.rst
index 616380d..e4cbe65 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -7,6 +7,8 @@
 
 - Add preliminary support for Python 3.12b4.
 
+- Add preliminary support for Python 3.13 as of 3.13a3.
+
 
 6.0 (2023-03-24)
 ================
diff --git a/appveyor.yml b/appveyor.yml
index 90ddfcb..5a7afc3 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -16,6 +16,9 @@ environment:
     - python: 310-x64
     - python: 311-x64
     - python: 312-x64
+    # `multibuild` cannot install non-final versions as they are not on
+    # ftp.python.org, so we skip Python 3.13 until its final release:
+    # - python: 313-x64
 
 install:
   - "SET PYTHONVERSION=%PYTHON%"
diff --git a/tox.ini b/tox.ini
index 2ab6e04..e884ae3 100644
--- a/tox.ini
+++ b/tox.ini
@@ -10,14 +10,17 @@ envlist =
     py310,py310-pure
     py311,py311-pure
     py312,py312-pure
+    py313,py313-pure
     pypy3
     docs
     coverage
 
 [testenv]
 usedevelop = true
+pip_pre = py313: true
 deps =
     py37: urllib3 < 2
+    Sphinx
 setenv =
     pure: PURE_PYTHON=1
     !pure-!pypy3: PURE_PYTHON=0
@@ -54,6 +57,7 @@ deps =
     check-manifest
     check-python-versions >= 0.20.0
     wheel
+commands_pre =
 commands =
     check-manifest
     check-python-versions