diff --git a/testsuite/MDAnalysisTests/coordinates/test_timestep_api.py b/testsuite/MDAnalysisTests/coordinates/test_timestep_api.py
index 83ef123df5b..077e30e90de 100644
--- a/testsuite/MDAnalysisTests/coordinates/test_timestep_api.py
+++ b/testsuite/MDAnalysisTests/coordinates/test_timestep_api.py
@@ -537,6 +537,13 @@ def test_wrong_pos_equality(self):
         assert ts1 != ts2
         assert ts2 != ts1
 
+    def test_no_pos_inequality(self):
+        ts1 = self.Timestep(self.size, positions=False)
+        ts2 = self.Timestep(self.size)
+
+        assert ts1 != ts2
+        assert ts2 != ts1
+
     def test_check_vels_equality(self):
         ts1 = self.Timestep(self.size, velocities=True)
         ts2 = self.Timestep(self.size, velocities=True)
@@ -595,6 +602,16 @@ def test_check_wrong_forces_equality(self):
         assert ts1 != ts2
         assert ts2 != ts1
 
+    @pytest.mark.parametrize('dim1', [None, [2., 2., 2., 90., 90., 90.]])
+    def test_dims_mismatch_inequality(self, dim1):
+        ts1 = self.Timestep(self.size)
+        ts1.dimensions = dim1
+        ts2 = self.Timestep(self.size)
+        ts2.dimensions = [1., 1., 1., 90., 90., 90.]
+
+        assert ts1 != ts2
+        assert ts2 != ts1
+
 
 # TODO: Merge this into generic Reader tests
 # These tests are all included in BaseReaderTest