diff --git a/firedrake/mg/mesh.py b/firedrake/mg/mesh.py
index 791775054d..b7f91fb679 100644
--- a/firedrake/mg/mesh.py
+++ b/firedrake/mg/mesh.py
@@ -204,7 +204,7 @@ def MeshHierarchy(mesh, refinement_levels,
 
 
 def ExtrudedMeshHierarchy(base_hierarchy, height, base_layer=-1, refinement_ratio=2, layers=None,
-                          kernel=None, extrusion_type='uniform', gdim=None,
+                          kernel=None, extrusion_type='uniform', periodic=False, gdim=None,
                           mesh_builder=firedrake.ExtrudedMesh):
     """Build a hierarchy of extruded meshes by extruding a hierarchy of meshes.
 
@@ -245,6 +245,7 @@ def ExtrudedMeshHierarchy(base_hierarchy, height, base_layer=-1, refinement_rati
     meshes = [mesh_builder(m, layer, kernel=kernel,
                            layer_height=height/layer,
                            extrusion_type=extrusion_type,
+                           periodic=periodic,
                            gdim=gdim)
               for (m, layer) in zip(base_hierarchy._meshes, layers)]
 
diff --git a/tests/firedrake/multigrid/test_poisson_gmg_extruded.py b/tests/firedrake/multigrid/test_poisson_gmg_extruded.py
index 68178ba969..659b0d17f6 100644
--- a/tests/firedrake/multigrid/test_poisson_gmg_extruded.py
+++ b/tests/firedrake/multigrid/test_poisson_gmg_extruded.py
@@ -2,8 +2,8 @@
 import pytest
 
 
-def run_poisson(typ):
-    if typ == "mg":
+def run_poisson(solver_type, periodic=False):
+    if solver_type == "mg":
         parameters = {"snes_type": "ksponly",
                       "ksp_type": "preonly",
                       "pc_type": "mg",
@@ -11,7 +11,7 @@ def run_poisson(typ):
                       "mg_levels_ksp_type": "chebyshev",
                       "mg_levels_ksp_max_it": 2,
                       "mg_levels_pc_type": "jacobi"}
-    elif typ == "fas":
+    elif solver_type == "fas":
         parameters = {"snes_type": "fas",
                       "snes_fas_type": "full",
                       "fas_coarse_snes_type": "ksponly",
@@ -25,7 +25,7 @@ def run_poisson(typ):
                       "fas_levels_ksp_convergence_test": "skip",
                       "snes_max_it": 1,
                       "snes_convergence_test": "skip"}
-    elif typ == "newtonfas":
+    elif solver_type == "newtonfas":
         parameters = {"snes_type": "newtonls",
                       "ksp_type": "preonly",
                       "pc_type": "none",
@@ -47,12 +47,12 @@ def run_poisson(typ):
                       "npc_snes_max_it": 1,
                       "npc_snes_convergence_test": "skip"}
     else:
-        raise RuntimeError("Unknown parameter set '%s' request", typ)
+        raise RuntimeError("Unknown parameter set '%s' request", solver_type)
 
     N = 10
     base = UnitIntervalMesh(N)
     basemh = MeshHierarchy(base, 2)
-    mh = ExtrudedMeshHierarchy(basemh, height=1, base_layer=N)
+    mh = ExtrudedMeshHierarchy(basemh, height=1, base_layer=N, periodic=periodic)
 
     V = FunctionSpace(mh[-1], 'CG', 2)
 
@@ -60,9 +60,8 @@ def run_poisson(typ):
     f = Function(V)
     v = TestFunction(V)
     F = inner(grad(u), grad(v))*dx - inner(f, v)*dx
-    bcs = [DirichletBC(V, 0, "on_boundary"),
-           DirichletBC(V, 0, "top"),
-           DirichletBC(V, 0, "bottom")]
+    subs = ("on_boundary",) if periodic else ("on_boundary", "top", "bottom")
+    bcs = [DirichletBC(V, 0, sub) for sub in subs]
     # Choose a forcing function such that the exact solution is not an
     # eigenmode.  This stresses the preconditioner much more.  e.g. 10
     # iterations of ilu fails to converge this problem sufficiently.
@@ -77,22 +76,12 @@ def run_poisson(typ):
     return norm(assemble(exact - u))
 
 
-@pytest.mark.parametrize("typ",
-                         ["mg", "fas", "newtonfas"])
-def test_poisson_gmg(typ):
-    assert run_poisson(typ) < 4e-6
+@pytest.mark.parallel([1, 3])
+@pytest.mark.parametrize("solver_type", ["mg", "fas", "newtonfas"])
+def test_poisson_gmg(solver_type):
+    assert run_poisson(solver_type) < 4e-6
 
 
-@pytest.mark.parallel
-def test_poisson_gmg_parallel_mg():
-    assert run_poisson("mg") < 4e-6
-
-
-@pytest.mark.parallel
-def test_poisson_gmg_parallel_fas():
-    assert run_poisson("fas") < 4e-6
-
-
-@pytest.mark.parallel
-def test_poisson_gmg_parallel_newtonfas():
-    assert run_poisson("newtonfas") < 4e-6
+@pytest.mark.parallel([1, 3])
+def test_poisson_gmg_periodic():
+    assert run_poisson("mg", periodic=True) < 4e-6