diff --git a/e2e/kind-config-multikind.yaml b/e2e/kind-config-smoke-tests.yaml
similarity index 100%
rename from e2e/kind-config-multikind.yaml
rename to e2e/kind-config-smoke-tests.yaml
diff --git a/e2e/run.sh b/e2e/run.sh
index 3462499fd..d6673610e 100755
--- a/e2e/run.sh
+++ b/e2e/run.sh
@@ -6,7 +6,7 @@ set -o nounset
 set -o pipefail
 IFS=$'\n\t'
 
-readonly cluster_name="kind-test-postgres-operator"
+readonly cluster_name="kind-smoke-test-postgres-operator"
 
 # avoid interference with previous test runs
 if [[ $(kind get clusters | grep "^${cluster_name}*") != "" ]]
@@ -14,7 +14,7 @@ then
   kind delete cluster --name ${cluster_name}
 fi
 
-kind create cluster --name ${cluster_name} --config ./e2e/kind-config-multikind.yaml
+kind create cluster --name ${cluster_name} --config ./e2e/kind-config-smoke-tests.yaml
 export KUBECONFIG="$(kind get kubeconfig-path --name=${cluster_name})"
 kubectl cluster-info
 
diff --git a/e2e/tests/test_example.py b/e2e/tests/test_smoke.py
similarity index 97%
rename from e2e/tests/test_example.py
rename to e2e/tests/test_smoke.py
index 35131d58a..baeae7b13 100755
--- a/e2e/tests/test_example.py
+++ b/e2e/tests/test_smoke.py
@@ -5,6 +5,9 @@ from pprint import pprint
 import subprocess
 
 class SmokeTestCase(unittest.TestCase):
+    '''
+    Test the most basic e2e functionality of the operator.
+    '''
 
     @classmethod
     def setUpClass(cls):