diff --git a/.github/workflows/tox.yml b/.github/workflows/tox.yml
index 93ba66f..68384f9 100644
--- a/.github/workflows/tox.yml
+++ b/.github/workflows/tox.yml
@@ -113,7 +113,11 @@ jobs:
         strategy:
             max-parallel: 3
             matrix:
-                python-version: [2.7, 3.4, 3.5]
+                # Packages are no longer available for the distribution that comes with the
+                # python:3.4 image, so we can't install the necessary dependencies. Eventually,
+                # this will happen to the others as well.
+                # EOL: [3.4]
+                python-version: [2.7, 3.5]
         container:
             image: python:${{ matrix.python-version }}
         steps:
diff --git a/tox.ini b/tox.ini
index 4138f49..fdc93f9 100644
--- a/tox.ini
+++ b/tox.ini
@@ -20,7 +20,7 @@ basepython =
   py3.7: python3.7
   py3.8: python3.8
   py3.9: python3.9
-  postgres: python3.5
+  postgres: python3.6
   windows: python3.6
 
 deps =
@@ -29,6 +29,8 @@ deps =
   cryptography1.8: cryptography==1.8.2
   cryptography2.3: cryptography==2.3.1
   py2.7: backports.test.support==0.1.1
+  py3.4: backports.test.support==0.1.1
+  py3.5: backports.test.support==0.1.1
 
 commands =
   sh -c '! tests/testapp/manage.py makemigrations --dry-run --exit --noinput'