diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 79142d500db0b130ba2fcc84c4bcc61c0b27bd09..aa420589a79406c7544f5edcea3874ba29475e7f 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -1,20 +1,3 @@
-Python 3.5 Titan X:
-  script:
-  - py_version=2.7
-  - export PYOPENCL_TEST=nvi:titan
-  - EXTRA_INSTALL="pybind11 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
-  - nvidia-titan-x
-  except:
-  - tags
-  allow_failure: True
-  artifacts:
-    reports:
-      junit: test/pytest.xml
-
 # Sumpy thus far is poorly parallelized (no workgroup-level parallelism), and
 # the Kepler has a tendency to hang as a result.
 #
@@ -50,15 +33,15 @@ Python 2.7 POCL:
     reports:
       junit: test/pytest.xml
 
-Python 3.5 POCL:
+Python 3.6 POCL:
   script:
-  - export PY_EXE=python3.5
+  - export PY_EXE=python3.6
   - export PYOPENCL_TEST=portable
   - export EXTRA_INSTALL="pybind11 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
+  - python3.6
   - pocl
   except:
   - tags
@@ -66,15 +49,15 @@ Python 3.5 POCL:
     reports:
       junit: test/pytest.xml
 
-Python 3.6 POCL:
+Python 3.7 POCL:
   script:
-  - export PY_EXE=python3.6
+  - export PY_EXE=python3.7
   - export PYOPENCL_TEST=portable
   - export EXTRA_INSTALL="pybind11 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:
-  - python3.6
+  - python3.7
   - pocl
   except:
   - tags
@@ -82,6 +65,23 @@ Python 3.6 POCL:
     reports:
       junit: test/pytest.xml
 
+Python 3.7 Titan X:
+  script:
+  - py_version=3.7
+  - export PYOPENCL_TEST=nvi:titan
+  - EXTRA_INSTALL="pybind11 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:
+  - python3.7
+  - nvidia-titan-x
+  except:
+  - tags
+  allow_failure: True
+  artifacts:
+    reports:
+      junit: test/pytest.xml
+
 Python 3.5 Conda:
   script:
   # Disable caching to ensure SymEngine code generation is exercised.