diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index 576fb48..912e801 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -1,5 +1,12 @@
 name: CI
 
+env:
+  # Current supported Python version. For applications, there is generally no
+  # reason to support multiple Python versions, so all actions are run with
+  # this version. Quote the version to avoid interpretation as a floating
+  # point number.
+  PYTHON_VERSION: "3.12"
+
 "on":
   merge_group: {}
   pull_request: {}
@@ -28,7 +35,7 @@ jobs:
       - name: Set up Python
         uses: actions/setup-python@v5
         with:
-          python-version: "3.12"
+          python-version: ${{ env.PYTHON_VERSION }}
 
       - name: Run pre-commit
         uses: pre-commit/action@v3.0.1
@@ -37,20 +44,15 @@ jobs:
     runs-on: ubuntu-latest
     timeout-minutes: 10
 
-    strategy:
-      matrix:
-        python:
-          - "3.12"
-
     steps:
       - uses: actions/checkout@v4
 
       - name: Run tox
         uses: lsst-sqre/run-tox@v1
         with:
-          python-version: ${{ matrix.python }}
+          python-version: ${{ env.PYTHON_VERSION }}
           tox-envs: "py,coverage-report,typing"
-          tox-plugins: "tox-docker tox-uv"
+          tox-requirements: requirements/tox.txt
 
   build:
     runs-on: ubuntu-latest
diff --git a/.github/workflows/periodic-ci.yaml b/.github/workflows/periodic-ci.yaml
index 19accc0..9ed4b08 100644
--- a/.github/workflows/periodic-ci.yaml
+++ b/.github/workflows/periodic-ci.yaml
@@ -5,6 +5,13 @@
 
 name: Periodic CI
 
+env:
+  # Current supported Python version. For applications, there is generally no
+  # reason to support multiple Python versions, so all actions are run with
+  # this version. Quote the version to avoid interpretation as a floating
+  # point number.
+  PYTHON_VERSION: "3.12"
+
 "on":
   schedule:
     - cron: "0 12 * * 1"
@@ -15,33 +22,32 @@ jobs:
     runs-on: ubuntu-latest
     timeout-minutes: 10
 
-    strategy:
-      matrix:
-        python:
-          - "3.12"
-
     steps:
       - uses: actions/checkout@v4
 
-      # Use the oldest supported version of Python to update dependencies,
-      # not the matrixed Python version, since this accurately reflects
-      # how dependencies should later be updated.
-      - name: Run neophile
-        uses: lsst-sqre/run-neophile@v1
+      - name: Set up Python
+        uses: actions/setup-python@v5
         with:
-          python-version: "3.12"
-          mode: update
+          python-version: ${{ env.PYTHON_VERSION }}
+
+      - name: Update dependencies
+        run: |
+          pip install --upgrade uv
+          uv venv
+          source .venv/bin/activate
+          make update-deps
+        shell: bash
 
       - name: Run tests in tox
         uses: lsst-sqre/run-tox@v1
         with:
           python-version: ${{ matrix.python }}
           tox-envs: "lint,typing,py"
+          tox-requirements: requirements/tox.txt
           use-cache: false
-          tox-plugins: "tox-docker tox-uv"
 
       - name: Report status
-        if: always()
+        if: failure()
         uses: ravsamhq/notify-slack-action@v2
         with:
           status: ${{ job.status }}