diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 00202e857..28adca005 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -10,13 +10,18 @@ on:
 
 jobs:
   build-and-test:
-    name: "Python ${{ matrix.python-version }} on ${{ matrix.os }}"
+    name: "Python ${{ matrix.python-version }} on ${{ matrix.os }} jax=${{ matrix.jax-version }}"
     runs-on: "${{ matrix.os }}"
 
     strategy:
       matrix:
         python-version: ["3.9", "3.10", "3.11"]
         os: [ubuntu-latest]
+        jax-version: [newest]
+        include:
+          - python-version: "3.9"
+            os: "ubuntu-latest"
+            jax-version: "0.4.27"  # Keep this in sync with version in pyproject.toml
 
     steps:
       - uses: "actions/checkout@v2"
@@ -26,7 +31,7 @@ jobs:
             cache: "pip"
             cache-dependency-path: 'pyproject.toml'
       - name: Run CI tests
-        run: bash test.sh
+        run: JAX_VERSION="${{ matrix.jax-version }}" bash test.sh
         shell: bash
   markdown-link-check:
     name: "Check links in markdown files"
diff --git a/pyproject.toml b/pyproject.toml
index 040d7b7de..775f8903d 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -32,8 +32,8 @@ classifiers = [
 dependencies = [
   "absl-py>=0.7.1",
   "chex>=0.1.86",
-  "jax>=0.4.26",
-  "jaxlib>=0.1.37",
+  "jax>=0.4.27",  # Keep this in sync with version in .github/workflows/tests.yml
+  "jaxlib>=0.4.27",
   "numpy>=1.18.0",
   "etils[epy]",
 ]
diff --git a/test.sh b/test.sh
index cea1657e5..6f536f8e1 100755
--- a/test.sh
+++ b/test.sh
@@ -41,6 +41,15 @@ pip install -q -e ".[test, examples]"
 pip install -q -e ".[dp-accounting]"
 pip install -q "dp-accounting>=0.1.1" --no-deps
 
+# Install the requested JAX version
+if [ "$JAX_VERSION" = "" ]; then
+  : # use version installed in requirements above
+elif [ "$JAX_VERSION" = "newest" ]; then
+  pip install -U jax jaxlib
+else
+  pip install "jax==${JAX_VERSION}" "jaxlib==${JAX_VERSION}"
+fi
+
 # Ensure optax was not installed by one of the dependencies above,
 # since if it is, the tests below will be run against that version instead of
 # the branch build.