diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 750bf6f4cc5018fc14c9195ec688d45bea21d129..e05717fc7f8c60089368951f71c0c323a1f4976d 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -1,12 +1,13 @@
-Python 3.5 POCL:
+Python 2.7 POCL:
   script:
-  - export PY_EXE=python3.5
+  - export PY_EXE=python2.7
   - export PYOPENCL_TEST=portable
+  - export PYTEST_ADDOPTS=-k-slowtest
   - export EXTRA_INSTALL="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:
@@ -16,6 +17,7 @@ Python 3.6 POCL:
   script:
   - export PY_EXE=python3.6
   - export PYOPENCL_TEST=portable
+  - export PYTEST_ADDOPTS=-k-slowtest
   - export EXTRA_INSTALL="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"
@@ -26,6 +28,36 @@ Python 3.6 POCL:
   except:
   - tags
 
+Python 2.7 POCL Slow:
+  script:
+  - export PY_EXE=python2.7
+  - export PYOPENCL_TEST=portable
+  - export PYTEST_ADDOPTS=-kslowtest
+  - export EXTRA_INSTALL="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
+  only:
+  - schedules
+
+Python 3.6 POCL Slow:
+  script:
+  - export PY_EXE=python3.6
+  - export PYOPENCL_TEST=portable
+  - export PYTEST_ADDOPTS=-kslowtest
+  - export EXTRA_INSTALL="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
+  - pocl
+  - large-node
+  only:
+  - schedules
+
 Python 3.6 POCL Examples:
   script:
   - export PY_EXE=python3.6
@@ -44,6 +76,7 @@ Python 3.5 Conda:
   script:
   - export SUMPY_FORCE_SYMBOLIC_BACKEND=symengine
   - CONDA_ENVIRONMENT=.test-conda-env-py3.yml
+  - export PYTEST_ADDOPTS=-k-slowtest
   - REQUIREMENTS_TXT=.test-conda-env-py3-requirements.txt
   - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project-within-miniconda.sh
   - ". ./build-and-test-py-project-within-miniconda.sh"
@@ -53,20 +86,6 @@ Python 3.5 Conda:
   except:
   - tags
 
-Python 2.7 POCL:
-  script:
-  - export PY_EXE=python2.7
-  - export PYOPENCL_TEST=portable
-  - export EXTRA_INSTALL="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 3.5 Conda Apple:
   script:
   - export LC_ALL=en_US.UTF-8
diff --git a/test/test_layer_pot_identity.py b/test/test_layer_pot_identity.py
index 942b6ed282ae1eb250c5d6bea645bc834dda84eb..4b05c682e0c126b8327ede581c5b4885cfbcaad6 100644
--- a/test/test_layer_pot_identity.py
+++ b/test/test_layer_pot_identity.py
@@ -233,12 +233,12 @@ class DynamicTestCase(object):
         if (self.geometry.mesh_name == "sphere"
                 and self.k != 0
                 and self.fmm_backend == "sumpy"):
-            pytest.skip("both direct eval and generating the FMM kernels "
+            raise ValueError("both direct eval and generating the FMM kernels "
                     "are too slow")
 
         if (self.geometry.mesh_name == "sphere"
                 and self.expr.zero_op_name == "green_grad"):
-            pytest.skip("does not achieve sufficient precision")
+            raise ValueError("does not achieve sufficient precision")
 
         if self.fmm_backend == "fmmlib":
             pytest.importorskip("pyfmmlib")
@@ -246,22 +246,28 @@ class DynamicTestCase(object):
 
 # {{{ integral identity tester
 
+
+@pytest.mark.slowtest
+@pytest.mark.parametrize("case", [
+        DynamicTestCase(SphereGeometry(), GreenExpr(), 0),
+])
+def test_identity_convergence_slow(case):
+    test_identity_convergence(case)
+
+
 @pytest.mark.parametrize("case", [
-    tc
-    for geom in [
-        StarfishGeometry(),
-        SphereGeometry(),
-        ]
-    for tc in [
-        DynamicTestCase(geom, GreenExpr(), 0),
-        DynamicTestCase(geom, GreenExpr(), 1.2),
-        DynamicTestCase(geom, GradGreenExpr(), 0),
-        DynamicTestCase(geom, GradGreenExpr(), 1.2),
-        DynamicTestCase(geom, ZeroCalderonExpr(), 0),
-
-        DynamicTestCase(geom, GreenExpr(), 0, fmm_backend="fmmlib"),
-        DynamicTestCase(geom, GreenExpr(), 1.2, fmm_backend="fmmlib"),
-        ]])
+        # 2d
+        DynamicTestCase(StarfishGeometry(), GreenExpr(), 0),
+        DynamicTestCase(StarfishGeometry(), GreenExpr(), 1.2),
+        DynamicTestCase(StarfishGeometry(), GradGreenExpr(), 0),
+        DynamicTestCase(StarfishGeometry(), GradGreenExpr(), 1.2),
+        DynamicTestCase(StarfishGeometry(), ZeroCalderonExpr(), 0),
+        DynamicTestCase(StarfishGeometry(), GreenExpr(), 0, fmm_backend="fmmlib"),
+        DynamicTestCase(StarfishGeometry(), GreenExpr(), 1.2, fmm_backend="fmmlib"),
+        # 3d
+        DynamicTestCase(SphereGeometry(), GreenExpr(), 0, fmm_backend="fmmlib"),
+        DynamicTestCase(SphereGeometry(), GreenExpr(), 1.2, fmm_backend="fmmlib")
+])
 def test_identity_convergence(ctx_getter,  case, visualize=False):
     logging.basicConfig(level=logging.INFO)