diff --git a/FIAT/restricted.py b/FIAT/restricted.py
index f72a731a..55215fa1 100644
--- a/FIAT/restricted.py
+++ b/FIAT/restricted.py
@@ -24,8 +24,40 @@ def __init__(self, dual, indices):
                                          for dof in dofs if dof in indices]
         nodes = [nodes_old[i] for i in indices]
         self._dual = dual
+        entity_permutations = self._restrict_entity_permutations(dual, entity_ids)
 
-        super().__init__(nodes, ref_el, entity_ids)
+        super().__init__(nodes, ref_el, entity_ids, entity_permutations)
+
+    @staticmethod
+    def _restrict_entity_permutations(dual, entity_ids):
+        """Inherit the entity permutations of the dofs kept by the restriction.
+
+        An entity whose dofs are all kept keeps their relative order, and so
+        permutes exactly as it did in ``dual``; an entity whose dofs are all
+        dropped permutes trivially. An entity that keeps only some of its dofs
+        has no permutation to inherit, since the dofs it drops may be the ones
+        the parent permutation maps the others onto, so no permutations are
+        given at all in that case.
+
+        :arg dual: the DualSet being restricted.
+        :arg entity_ids: the entity ids of the restricted dual set.
+        :returns: the entity permutations, or None if they cannot be inherited.
+        """
+        permutations_old = dual.entity_permutations
+        if permutations_old is None:
+            return None
+        entity_permutations = {}
+        for d, entities in dual.get_entity_ids().items():
+            entity_permutations[d] = {}
+            for entity, dofs in entities.items():
+                perms = permutations_old[d][entity]
+                if len(entity_ids[d][entity]) == len(dofs):
+                    entity_permutations[d][entity] = {o: list(p) for o, p in perms.items()}
+                elif len(entity_ids[d][entity]) == 0:
+                    entity_permutations[d][entity] = {o: [] for o in perms}
+                else:
+                    return None
+        return entity_permutations
 
     def get_indices(self, restriction_domain, take_closure=True):
         """Return the list of dofs with support on a given restriction domain.
diff --git a/test/FIAT/unit/test_orientation.py b/test/FIAT/unit/test_orientation.py
index 7f9da514..b83b0798 100644
--- a/test/FIAT/unit/test_orientation.py
+++ b/test/FIAT/unit/test_orientation.py
@@ -1,4 +1,5 @@
 import pytest
+from FIAT import DiscontinuousLagrange, Lagrange, RestrictedElement
 from FIAT.reference_element import Point, UFCInterval, UFCTriangle, UFCQuadrilateral
 from FIAT.orientation_utils import make_entity_permutations_tensorproduct
 
@@ -69,3 +70,33 @@ def test_orientation_cell_orientation_reflection_map(cell):
                      (1, 0, 1): 0,
                      (1, 1, 0): 0,
                      (1, 1, 1): 1}
+
+
+@pytest.mark.parametrize("degree", [1, 2, 3, 4, 5])
+def test_orientation_restricted_element(degree):
+    # A restriction keeps the relative order of the dofs on the entities it
+    # keeps, so those entities must permute exactly as they did before it.
+    element = Lagrange(UFCTriangle(), degree)
+    restricted = RestrictedElement(element, restriction_domain="facet")
+
+    permutations = element.dual.get_entity_permutations()
+    restricted_permutations = restricted.dual.get_entity_permutations()
+
+    for dim in (0, 1):
+        for entity in permutations[dim]:
+            assert restricted_permutations[dim][entity] == permutations[dim][entity]
+    # The cell is dropped, so it has no dofs left to permute.
+    for orientation, perm in restricted_permutations[2][0].items():
+        assert perm == []
+
+
+def test_orientation_restricted_element_partial_entity():
+    # An entity that keeps only some of its dofs has no permutation to
+    # inherit, since the dofs it drops may be where the parent permutation
+    # sends the ones it keeps, so no permutations are reported at all.
+    element = DiscontinuousLagrange(UFCTriangle(), 1)
+    restricted = RestrictedElement(element, indices=[0])
+
+    assert restricted.dual.entity_permutations is None
+    with pytest.raises(NotImplementedError):
+        restricted.dual.get_entity_permutations()