diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 69021af24fd195bcc432ac9a38537106ec4f986d..136d21730301d00eb1559d2a88818eba25d1f8e8 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -26,28 +26,14 @@ Python 2.7:
     reports:
       junit: test/pytest.xml
 
-Python 3.6:
+Python 3:
   script:
-  - py_version=3.6
+  - py_version=3
   - export EXTRA_INSTALL="numpy"
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
   - ". ./build-and-test-py-project.sh"
   tags:
-  - python3.6
-  except:
-  - tags
-  artifacts:
-    reports:
-      junit: test/pytest.xml
-
-Python 3.7:
-  script:
-  - py_version=3.7
-  - export EXTRA_INSTALL="numpy"
-  - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
-  - ". ./build-and-test-py-project.sh"
-  tags:
-  - python3.7
+  - python3
   except:
   - tags
   artifacts:
@@ -59,18 +45,18 @@ Flake8:
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/prepare-and-run-flake8.sh
   - ". ./prepare-and-run-flake8.sh pytools test"
   tags:
-  - python3.6
+  - python3
   except:
   - tags
 
 Pylint:
   script:
   - EXTRA_INSTALL="pymbolic matplotlib mpi4py"
-  - py_version=3.6
+  - py_version=3
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/prepare-and-run-pylint.sh
   - ". ./prepare-and-run-pylint.sh pytools test/test_*.py"
   tags:
-  - python3.6
+  - python3
   except:
   - tags
 
@@ -80,7 +66,7 @@ Documentation:
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-docs.sh
   - ". ./build-docs.sh"
   tags:
-  - python3.5
+  - python3
   only:
   - master