diff --git a/devito/finite_differences/derivative.py b/devito/finite_differences/derivative.py
index 9e13454170..889cfbfdbc 100644
--- a/devito/finite_differences/derivative.py
+++ b/devito/finite_differences/derivative.py
@@ -138,6 +138,10 @@ def _process_kwargs(cls, expr, *dims, **kwargs):
             variable_count = [sympy.Tuple(s, dims.count(s))
                               for s in filter_ordered(dims)]
             return dims, deriv_orders, fd_orders, variable_count
+
+        # Sanitise `dims`. ((x, 2), (y, 0)) is valid input, but (y, 0) should be dropped.
+        dims = tuple(d for d in dims if not (isinstance(d, Iterable) and d[1] == 0))
+
         # Check `dims`. It can be a single Dimension, an iterable of Dimensions, or even
         # an iterable of 2-tuple (Dimension, deriv_order)
         if len(dims) == 0:
diff --git a/tests/test_derivatives.py b/tests/test_derivatives.py
index e6f5849925..0ee95450c7 100644
--- a/tests/test_derivatives.py
+++ b/tests/test_derivatives.py
@@ -632,6 +632,27 @@ def test_substitution(self):
         assert f1 is not f2
         assert f1.subs(f2, -1) == -1
 
+    def test_zero_spec(self):
+        """
+        Test that derivatives specified as Derivative(f, (x, 2), (y, 0)) are
+        correctly handled.
+        """
+        grid = Grid((11, 11))
+        x, y = grid.dimensions
+        f = Function(name="f", grid=grid, space_order=4)
+        # Check that both specifications match
+        drv0 = Derivative(f, (x, 2))
+        drv1 = Derivative(f, (x, 2), (y, 0))
+        assert drv0.dims == drv1.dims
+        assert drv0.fd_order == drv1.fd_order
+        assert drv0.deriv_order == drv1.deriv_order
+
+        # Check that substitution can applied correctly
+        expr0 = drv0 + 1
+        expr1 = drv1 + 1
+        assert expr0.subs(drv0, drv1) == expr1
+        assert expr1.subs(drv1, drv0) == expr0
+
 
 class TestTwoStageEvaluation(object):