diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 9e883d08c97d1396e3d38f4555768f34f8c57032..417d83de653879c1fa9349cb2110c1af1168c071 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
   - 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=3.7m
-  - 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:
@@ -60,7 +46,7 @@ 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
 
@@ -69,6 +55,6 @@ Flake8:
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/prepare-and-run-flake8.sh
   - ". ./prepare-and-run-flake8.sh pyopencl test"
   tags:
-  - python3.5
+  - python3
   except:
   - tags