diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 9526444ebafca74473618978b184ea0ebad235e9..4b926a9fd416bb86b5a24482373268844672b357 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -1,12 +1,12 @@
-Python 3.5 POCL:
+Python 2.7 POCL:
   script:
-  - export PY_EXE=python3.5
+  - export PY_EXE=python2.7
   - export PYOPENCL_TEST=portable
-  - export EXTRA_INSTALL="pybind11 numpy scipy mako"
+  - export EXTRA_INSTALL="pybind11 scipy numpy mako"
   - 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:
-  - python3.5
+  - python2.7
   - pocl
   - large-node
   except:
@@ -26,6 +26,20 @@ Python 3.6 POCL:
   except:
   - tags
 
+Python 3.7 POCL:
+  script:
+  - export PY_EXE=python3.7
+  - export PYOPENCL_TEST=portable
+  - export EXTRA_INSTALL="pybind11 numpy scipy mako"
+  - 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
+  - pocl
+  - large-node
+  except:
+  - tags
+
 Python 3.6 POCL Examples:
   script:
   - export PY_EXE=python3.6
@@ -53,20 +67,6 @@ Python 3.6 Conda:
   except:
   - tags
 
-Python 2.7 POCL:
-  script:
-  - export PY_EXE=python2.7
-  - export PYOPENCL_TEST=portable
-  - export EXTRA_INSTALL="pybind11 scipy numpy mako"
-  - 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:
-  - python2.7
-  - pocl
-  - large-node
-  except:
-  - tags
-
 Python 3.6 Conda Apple:
   script:
   - export LC_ALL=en_US.UTF-8