diff --git a/.github/workflows/python-CI.yml b/.github/workflows/python-CI.yml
index ab11e13718..344815be02 100644
--- a/.github/workflows/python-CI.yml
+++ b/.github/workflows/python-CI.yml
@@ -166,11 +166,19 @@ jobs:
     strategy:
       matrix:
         py: [ 3.9, 3.12 ]
+        db: [ sqlite, postgresql ]
         os: [ ubuntu-latest, windows-latest, macos-13 ]
+        exclude:
+          - db: postgresql
+            os: windows-latest
+          - db: postgresql
+            os: macos-13
+    env:
+      CI_TEST_DB_BACKEND: ${{ matrix.db }}
     services:
       postgres:
         # Applying this workaround: https://github.com/actions/runner/issues/822
-        image: ${{ (matrix.os == 'ubuntu-latest') && 'postgres:12' || '' }}
+        image: ${{ (matrix.db == 'postgresql') && 'postgres:12' || '' }}
         env:
           POSTGRES_PASSWORD: phoenix
         options: >-
diff --git a/.github/workflows/python-cron.yml b/.github/workflows/python-cron.yml
index 4160c6942b..249bdb2266 100644
--- a/.github/workflows/python-cron.yml
+++ b/.github/workflows/python-cron.yml
@@ -8,6 +8,8 @@ on:
 jobs:
   integration-test:
     runs-on: ubuntu-latest
+    env:
+      CI_TEST_DB_BACKEND: postgresql
     services:
       postgres:
         image: postgres:12
diff --git a/tests/integration/_helpers.py b/tests/integration/_helpers.py
index b4ad8364d7..baf13293c0 100644
--- a/tests/integration/_helpers.py
+++ b/tests/integration/_helpers.py
@@ -656,13 +656,7 @@ def _random_schema(
     url: URL,
 ) -> Iterator[str]:
     engine = create_engine(url.set(drivername="postgresql+psycopg"))
-    try:
-        engine.connect().close()
-    except OperationalError as exc:
-        if "too many clients" in str(exc):
-            pass
-        else:
-            pytest.skip(f"PostgreSQL unavailable: {exc}")
+    engine.connect().close()
     engine.dispose()
     schema = f"_{secrets.token_hex(15)}"
     yield schema
diff --git a/tests/integration/conftest.py b/tests/integration/conftest.py
index 1bd602d468..8c7fb8febd 100644
--- a/tests/integration/conftest.py
+++ b/tests/integration/conftest.py
@@ -58,18 +58,14 @@ def _(used: List[int]) -> Iterator[int]:
     return _([])
 
 
-@pytest.fixture(
-    scope="session",
-    params=[
-        pytest.param("sqlite:///:memory:", id="sqlite"),
-        pytest.param(
-            "postgresql://127.0.0.1:5432/postgres?user=postgres&password=phoenix",
-            id="postgresql",
-        ),
-    ],
-)
+@pytest.fixture(scope="session")
 def _sql_database_url(request: SubRequest) -> URL:
-    return make_url(request.param)
+    backend = os.getenv("CI_TEST_DB_BACKEND")
+    if not backend or backend == "sqlite":
+        return make_url("sqlite:///:memory:")
+    if backend == "postgresql":
+        return make_url("postgresql://127.0.0.1:5432/postgres?user=postgres&password=phoenix")
+    pytest.fail(f"Unknown database backend: {backend}")
 
 
 @pytest.fixture(scope="session", params=["http", "grpc"])
diff --git a/tox.ini b/tox.ini
index 1b0eca55be..2697b2493f 100644
--- a/tox.ini
+++ b/tox.ini
@@ -29,6 +29,8 @@ commands =
   ; pytest -ra -x {posargs:.}
 
 [testenv:ci_integration_tests]
+pass_env =
+  CI_TEST_DB_BACKEND
 changedir = tests/integration
 deps =
   -r requirements/integration-tests.txt
@@ -63,6 +65,8 @@ commands =
   ; pytest {posargs:.}
 
 [testenv:integration_tests]
+pass_env =
+  CI_TEST_DB_BACKEND
 changedir = tests/integration
 deps =
   -r requirements/integration-tests.txt