diff --git a/test/tests/functions/function_file_format/function_file_format_test.i b/test/tests/functions/function_file_format/function_file_format_test.i
index 1b1e870a3370..099af041cf01 100644
--- a/test/tests/functions/function_file_format/function_file_format_test.i
+++ b/test/tests/functions/function_file_format/function_file_format_test.i
@@ -21,6 +21,10 @@
 # At time = 0, the variable = 0, at time = 1, variable = 4 and so on.
 [Mesh]
   file = cube.e
+  # This problem only has 1 element, so using ParallelMesh in parallel
+  # isn't really an option, and we don't care that much about ParallelMesh
+  # in serial.
+  distribution = serial
 []
 
 [Variables]
diff --git a/test/tests/utils/2d_linear_interpolation/2d_linear_interpolation_test.i b/test/tests/utils/2d_linear_interpolation/2d_linear_interpolation_test.i
index f775c74e2a2d..93d0d6221fa6 100644
--- a/test/tests/utils/2d_linear_interpolation/2d_linear_interpolation_test.i
+++ b/test/tests/utils/2d_linear_interpolation/2d_linear_interpolation_test.i
@@ -98,6 +98,10 @@
 #
 [Mesh]
   file = cube.e
+  # This problem only has 1 element, so using ParallelMesh in parallel
+  # isn't really an option, and we don't care that much about ParallelMesh
+  # in serial.
+  distribution = serial
 []
 
 [Variables]
diff --git a/test/tests/variables/curvilinear_element/curvilinear_element_test.i b/test/tests/variables/curvilinear_element/curvilinear_element_test.i
index cdac7f76c548..4ba80b9d8f05 100644
--- a/test/tests/variables/curvilinear_element/curvilinear_element_test.i
+++ b/test/tests/variables/curvilinear_element/curvilinear_element_test.i
@@ -1,5 +1,9 @@
 [Mesh]
   file = curvi.e
+  # This mesh only has one element.  It does seem to work if you
+  # use SerialMesh on two processors, but it hangs with ParallelMesh
+  # on two processors.
+  distribution = serial
 []
 
 [Variables]
diff --git a/test/tests/variables/fe_hermite/hermite-3-3d.i b/test/tests/variables/fe_hermite/hermite-3-3d.i
index 04de1431913c..adadc8ee5162 100644
--- a/test/tests/variables/fe_hermite/hermite-3-3d.i
+++ b/test/tests/variables/fe_hermite/hermite-3-3d.i
@@ -11,6 +11,10 @@
   ny = 1
   nz = 1
   elem_type = HEX27
+  # This problem only has 1 element, so using ParallelMesh in parallel
+  # isn't really an option, and we don't care that much about ParallelMesh
+  # in serial.
+  distribution = serial
 []
 
 [Functions]
diff --git a/test/tests/variables/fe_hier/hier-2-3d.i b/test/tests/variables/fe_hier/hier-2-3d.i
index 891126d72bce..c56b130863b8 100644
--- a/test/tests/variables/fe_hier/hier-2-3d.i
+++ b/test/tests/variables/fe_hier/hier-2-3d.i
@@ -11,6 +11,10 @@
   ny = 1
   nz = 1
   elem_type = HEX27
+  # This problem only has 1 element, so using ParallelMesh in parallel
+  # isn't really an option, and we don't care that much about ParallelMesh
+  # in serial.
+  distribution = serial
 []
 
 [Functions]
diff --git a/test/tests/variables/fe_hier/hier-3-3d.i b/test/tests/variables/fe_hier/hier-3-3d.i
index ef2c612b428d..03318083abea 100644
--- a/test/tests/variables/fe_hier/hier-3-3d.i
+++ b/test/tests/variables/fe_hier/hier-3-3d.i
@@ -11,6 +11,10 @@
   ny = 1
   nz = 1
   elem_type = HEX27
+  # This problem only has 1 element, so using ParallelMesh in parallel
+  # isn't really an option, and we don't care that much about ParallelMesh
+  # in serial.
+  distribution = serial
 []
 
 [Functions]