diff --git a/traitsui/editor_factory.py b/traitsui/editor_factory.py
index 10a835b1f..3a0a63072 100644
--- a/traitsui/editor_factory.py
+++ b/traitsui/editor_factory.py
@@ -309,15 +309,3 @@ class EditorWithListFactory(EditorFactory):
 
     #: Name of the trait on 'object' containing the enumeration data
     name = Str()
-
-    #: Fired when the **values** trait has been updated:
-    values_modified = Event()
-
-    def _values_changed(self):
-        """ Recomputes the mappings whenever the **values** trait is changed.
-        """
-        self._names, self._mapping, self._inverse_mapping = enum_values_changed(
-            self.values, strfunc=self.string_value
-        )
-
-        self.values_modified = True
diff --git a/traitsui/qt4/enum_editor.py b/traitsui/qt4/enum_editor.py
index d017030b9..d20f484f0 100644
--- a/traitsui/qt4/enum_editor.py
+++ b/traitsui/qt4/enum_editor.py
@@ -59,7 +59,8 @@ class BaseEditor(Editor):
     # -------------------------------------------------------------------------
 
     def values_changed(self):
-        """ Recomputes the cached data based on the underlying enumeration model.
+        """ Recomputes the cached data based on the underlying enumeration model
+            or the values of the factory.
         """
         self._names, self._mapping, self._inverse_mapping = enum_values_changed(
             self._value(), self.string_value
@@ -91,8 +92,10 @@ def init(self, parent):
                 self._values_changed, " " + self._name, dispatch="ui"
             )
         else:
+            self._value = lambda: self.factory.values
+            self.values_changed()
             factory.on_trait_change(
-                self.rebuild_editor, "values_modified", dispatch="ui"
+                self._values_changed, "values", dispatch="ui"
             )
 
     def dispose(self):
@@ -104,7 +107,7 @@ def dispose(self):
             )
         else:
             self.factory.on_trait_change(
-                self.rebuild_editor, "values_modified", remove=True
+                self._values_changed, "values", remove=True
             )
 
         super(BaseEditor, self).dispose()
@@ -118,31 +121,23 @@ def dispose(self):
     def _get_names(self):
         """ Gets the current set of enumeration names.
         """
-        if self._object is None:
-            return self.factory._names
-
         return self._names
 
     def _get_mapping(self):
         """ Gets the current mapping.
         """
-        if self._object is None:
-            return self.factory._mapping
-
         return self._mapping
 
     def _get_inverse_mapping(self):
         """ Gets the current inverse mapping.
         """
-        if self._object is None:
-            return self.factory._inverse_mapping
-
         return self._inverse_mapping
 
     # Trait change handlers --------------------------------------------------
 
     def _values_changed(self):
-        """ Handles the underlying object model's enumeration set being changed.
+        """ Handles the underlying object model's enumeration set or factory's
+            values being changed.
         """
         self.values_changed()
         self.rebuild_editor()
diff --git a/traitsui/qt4/image_enum_editor.py b/traitsui/qt4/image_enum_editor.py
index 1d810edf4..21d925637 100644
--- a/traitsui/qt4/image_enum_editor.py
+++ b/traitsui/qt4/image_enum_editor.py
@@ -57,6 +57,8 @@ def init(self, parent):
         """ Finishes initializing the editor by creating the underlying toolkit
             widget.
         """
+        super(ReadonlyEditor, self).init(parent)
+
         self.control = QtGui.QLabel()
         self.control.setPixmap(self.get_pixmap(self.str_value))
         self.set_tooltip()
@@ -67,6 +69,12 @@ def update_editor(self):
         """
         self.control.setPixmap(self.get_pixmap(self.str_value))
 
+    def rebuild_editor(self):
+        """ Rebuilds the contents of the editor whenever the original factory
+            object's **values** trait changes.
+        """
+        pass
+
 
 class SimpleEditor(BaseEditor, SimpleEnumEditor):
     """ Simple style of image enumeration editor, which displays a combo box.
diff --git a/traitsui/qt4/set_editor.py b/traitsui/qt4/set_editor.py
index 8afd5c869..4bb93e3a1 100644
--- a/traitsui/qt4/set_editor.py
+++ b/traitsui/qt4/set_editor.py
@@ -76,8 +76,10 @@ def init(self, parent):
                 self._values_changed, self._name, dispatch="ui"
             )
         else:
+            self._value = lambda: self.factory.values
+            self.values_changed()
             factory.on_trait_change(
-                self.update_editor, "values_modified", dispatch="ui"
+                self._values_changed, "values", dispatch="ui"
             )
 
         blayout = QtGui.QVBoxLayout()
@@ -120,25 +122,16 @@ def init(self, parent):
     def _get_names(self):
         """ Gets the current set of enumeration names.
         """
-        if self._object is None:
-            return self.factory._names
-
         return self._names
 
     def _get_mapping(self):
         """ Gets the current mapping.
         """
-        if self._object is None:
-            return self.factory._mapping
-
         return self._mapping
 
     def _get_inverse_mapping(self):
         """ Gets the current inverse mapping.
         """
-        if self._object is None:
-            return self.factory._inverse_mapping
-
         return self._inverse_mapping
 
     def _create_listbox(self, col, handler1, handler2, title):
@@ -171,14 +164,16 @@ def _create_button(self, label, layout, handler):
         return button
 
     def values_changed(self):
-        """ Recomputes the cached data based on the underlying enumeration model.
+        """ Recomputes the cached data based on the underlying enumeration model
+            or the values of the factory.
         """
         self._names, self._mapping, self._inverse_mapping = enum_values_changed(
             self._value(), self.string_value
         )
 
     def _values_changed(self):
-        """ Handles the underlying object model's enumeration set being changed.
+        """ Handles the underlying object model's enumeration set or factory's
+            values being changed.
         """
         self.values_changed()
         self.update_editor()
@@ -260,7 +255,7 @@ def dispose(self):
             )
         else:
             self.factory.on_trait_change(
-                self.update_editor, "values_modified", remove=True
+                self._values_changed, "values", remove=True
             )
 
         self.context_object.on_trait_change(
diff --git a/traitsui/tests/editors/test_enum_editor.py b/traitsui/tests/editors/test_enum_editor.py
index 01f856528..617c138d3 100644
--- a/traitsui/tests/editors/test_enum_editor.py
+++ b/traitsui/tests/editors/test_enum_editor.py
@@ -196,17 +196,10 @@ class IntEnumModel(HasTraits):
         with store_exceptions_on_all_threads():
             editor = self.setup_ui(IntEnumModel(), formatted_view)
 
-            # FIXME issue enthought/traitsui#782
-            with self.assertRaises(AssertionError):
-                self.assertEqual(editor.names, ["FALSE", "TRUE"])
-                self.assertEqual(editor.mapping, {"FALSE": 0, "TRUE": 1})
-                self.assertEqual(
-                    editor.inverse_mapping, {0: "FALSE", 1: "TRUE"}
-                )
-            self.assertEqual(editor.names, ["0", "1"])
-            self.assertEqual(editor.mapping, {"0": 0, "1": 1})
+            self.assertEqual(editor.names, ["FALSE", "TRUE"])
+            self.assertEqual(editor.mapping, {"FALSE": 0, "TRUE": 1})
             self.assertEqual(
-                editor.inverse_mapping, {0: "0", 1: "1"}
+                editor.inverse_mapping, {0: "FALSE", 1: "TRUE"}
             )
 
             enum_editor_factory.values = [1, 0]
@@ -238,47 +231,19 @@ class IntEnumModel(HasTraits):
         with store_exceptions_on_all_threads():
             editor = self.setup_ui(model, formatted_view)
 
-            # FIXME issue enthought/traitsui#835
-            if is_current_backend_wx():
-                with self.assertRaises(AssertionError):
-                    self.assertEqual(editor.names, ["FALSE", "TRUE"])
-                    self.assertEqual(editor.mapping, {"FALSE": 0, "TRUE": 1})
-                    self.assertEqual(
-                        editor.inverse_mapping, {0: "FALSE", 1: "TRUE"}
-                    )
-                self.assertEqual(editor.names, ["0", "1"])
-                self.assertEqual(editor.mapping, {"0": 0, "1": 1})
-                self.assertEqual(
-                    editor.inverse_mapping, {0: "0", 1: "1"}
-                )
-            else:
-                self.assertEqual(editor.names, ["FALSE", "TRUE"])
-                self.assertEqual(editor.mapping, {"FALSE": 0, "TRUE": 1})
-                self.assertEqual(
-                    editor.inverse_mapping, {0: "FALSE", 1: "TRUE"}
-                )
+            self.assertEqual(editor.names, ["FALSE", "TRUE"])
+            self.assertEqual(editor.mapping, {"FALSE": 0, "TRUE": 1})
+            self.assertEqual(
+                editor.inverse_mapping, {0: "FALSE", 1: "TRUE"}
+            )
 
             model.possible_values = [1, 0]
 
-            # FIXME issue enthought/traitsui#835
-            if is_current_backend_wx():
-                with self.assertRaises(AssertionError):
-                    self.assertEqual(editor.names, ["TRUE", "FALSE"])
-                    self.assertEqual(editor.mapping, {"TRUE": 1, "FALSE": 0})
-                    self.assertEqual(
-                        editor.inverse_mapping, {1: "TRUE", 0: "FALSE"}
-                    )
-                self.assertEqual(editor.names, ["1", "0"])
-                self.assertEqual(editor.mapping, {"1": 1, "0": 0})
-                self.assertEqual(
-                    editor.inverse_mapping, {1: "1", 0: "0"}
-                )
-            else:
-                self.assertEqual(editor.names, ["TRUE", "FALSE"])
-                self.assertEqual(editor.mapping, {"TRUE": 1, "FALSE": 0})
-                self.assertEqual(
-                    editor.inverse_mapping, {1: "TRUE", 0: "FALSE"}
-                )
+            self.assertEqual(editor.names, ["TRUE", "FALSE"])
+            self.assertEqual(editor.mapping, {"TRUE": 1, "FALSE": 0})
+            self.assertEqual(
+                editor.inverse_mapping, {1: "TRUE", 0: "FALSE"}
+            )
 
     def test_simple_editor_mapping_values(self):
         self.check_enum_mappings_value_change("simple", "radio")
diff --git a/traitsui/tests/editors/test_image_enum_editor.py b/traitsui/tests/editors/test_image_enum_editor.py
index 20f15a05c..6e2d57172 100644
--- a/traitsui/tests/editors/test_image_enum_editor.py
+++ b/traitsui/tests/editors/test_image_enum_editor.py
@@ -155,25 +155,14 @@ def check_enum_mappings_value_change(self, style):
         with store_exceptions_on_all_threads():
             editor = self.setup_ui(EnumModel(), formatted_view)
 
-            # FIXME issue enthought/traitsui#782
-            with self.assertRaises(AssertionError):
-                self.assertEqual(editor.names, ["TOP LEFT", "TOP RIGHT"])
-                self.assertEqual(
-                    editor.mapping,
-                    {"TOP LEFT": "top left", "TOP RIGHT": "top right"}
-                )
-                self.assertEqual(
-                    editor.inverse_mapping,
-                    {"top left": "TOP LEFT", "top right": "TOP RIGHT"}
-                )
-            self.assertEqual(editor.names, ["top left", "top right"])
+            self.assertEqual(editor.names, ["TOP LEFT", "TOP RIGHT"])
             self.assertEqual(
                 editor.mapping,
-                {"top left": "top left", "top right": "top right"}
+                {"TOP LEFT": "top left", "TOP RIGHT": "top right"}
             )
             self.assertEqual(
                 editor.inverse_mapping,
-                {"top left": "top left", "top right": "top right"}
+                {"top left": "TOP LEFT", "top right": "TOP RIGHT"}
             )
 
             image_enum_editor_factory.values = ["top right", "top left"]
diff --git a/traitsui/tests/editors/test_set_editor.py b/traitsui/tests/editors/test_set_editor.py
index f64ab280c..599eef763 100644
--- a/traitsui/tests/editors/test_set_editor.py
+++ b/traitsui/tests/editors/test_set_editor.py
@@ -170,17 +170,10 @@ class IntListModel(HasTraits):
         with store_exceptions_on_all_threads():
             editor = self.setup_ui(IntListModel(), formatted_view)
 
-            # FIXME issue enthought/traitsui#782
-            with self.assertRaises(AssertionError):
-                self.assertEqual(editor.names, ["FALSE", "TRUE"])
-                self.assertEqual(editor.mapping, {"FALSE": 0, "TRUE": 1})
-                self.assertEqual(
-                    editor.inverse_mapping, {0: "FALSE", 1: "TRUE"}
-                )
-            self.assertEqual(editor.names, ["0", "1"])
-            self.assertEqual(editor.mapping, {"0": 0, "1": 1})
+            self.assertEqual(editor.names, ["FALSE", "TRUE"])
+            self.assertEqual(editor.mapping, {"FALSE": 0, "TRUE": 1})
             self.assertEqual(
-                editor.inverse_mapping, {0: "0", 1: "1"}
+                editor.inverse_mapping, {0: "FALSE", 1: "TRUE"}
             )
 
             set_editor_factory.values = [1, 0]
@@ -211,47 +204,19 @@ class IntListModel(HasTraits):
         with store_exceptions_on_all_threads():
             editor = self.setup_ui(model, formatted_view)
 
-            # FIXME issue enthought/traitsui#835
-            if is_current_backend_wx():
-                with self.assertRaises(AssertionError):
-                    self.assertEqual(editor.names, ["FALSE", "TRUE"])
-                    self.assertEqual(editor.mapping, {"FALSE": 0, "TRUE": 1})
-                    self.assertEqual(
-                        editor.inverse_mapping, {0: "FALSE", 1: "TRUE"}
-                    )
-                self.assertEqual(editor.names, ["0", "1"])
-                self.assertEqual(editor.mapping, {"0": 0, "1": 1})
-                self.assertEqual(
-                    editor.inverse_mapping, {0: "0", 1: "1"}
-                )
-            else:
-                self.assertEqual(editor.names, ["FALSE", "TRUE"])
-                self.assertEqual(editor.mapping, {"FALSE": 0, "TRUE": 1})
-                self.assertEqual(
-                    editor.inverse_mapping, {0: "FALSE", 1: "TRUE"}
-                )
+            self.assertEqual(editor.names, ["FALSE", "TRUE"])
+            self.assertEqual(editor.mapping, {"FALSE": 0, "TRUE": 1})
+            self.assertEqual(
+                editor.inverse_mapping, {0: "FALSE", 1: "TRUE"}
+            )
 
             model.possible_values = [1, 0]
 
-            # FIXME issue enthought/traitsui#835
-            if is_current_backend_wx():
-                with self.assertRaises(AssertionError):
-                    self.assertEqual(editor.names, ["TRUE", "FALSE"])
-                    self.assertEqual(editor.mapping, {"TRUE": 1, "FALSE": 0})
-                    self.assertEqual(
-                        editor.inverse_mapping, {1: "TRUE", 0: "FALSE"}
-                    )
-                self.assertEqual(editor.names, ["1", "0"])
-                self.assertEqual(editor.mapping, {"1": 1, "0": 0})
-                self.assertEqual(
-                    editor.inverse_mapping, {1: "1", 0: "0"}
-                )
-            else:
-                self.assertEqual(editor.names, ["TRUE", "FALSE"])
-                self.assertEqual(editor.mapping, {"TRUE": 1, "FALSE": 0})
-                self.assertEqual(
-                    editor.inverse_mapping, {1: "TRUE", 0: "FALSE"}
-                )
+            self.assertEqual(editor.names, ["TRUE", "FALSE"])
+            self.assertEqual(editor.mapping, {"TRUE": 1, "FALSE": 0})
+            self.assertEqual(
+                editor.inverse_mapping, {1: "TRUE", 0: "FALSE"}
+            )
 
 
 @skip_if_null
diff --git a/traitsui/wx/enum_editor.py b/traitsui/wx/enum_editor.py
index bb7894d62..80049dd76 100644
--- a/traitsui/wx/enum_editor.py
+++ b/traitsui/wx/enum_editor.py
@@ -29,12 +29,13 @@
 # traitsui.editors.drop_editor file.
 from traitsui.editors.enum_editor import ToolkitEditorFactory
 
+from traitsui.helper import enum_values_changed
+
 from .editor import Editor
 
 from .constants import OKColor, ErrorColor
 
 from .helper import (
-    enum_values_changed,
     TraitsUIPanel,
     disconnect,
     disconnect_no_id,
@@ -82,32 +83,25 @@ def init(self, parent):
                 self._values_changed, " " + self._name, dispatch="ui"
             )
         else:
+            self._value = lambda: self.factory.values
+            self.values_changed()
             factory.on_trait_change(
-                self.rebuild_editor, "values_modified", dispatch="ui"
+                self._values_changed, "values", dispatch="ui"
             )
 
     def _get_names(self):
         """ Gets the current set of enumeration names.
         """
-        if self._object is None:
-            return self.factory._names
-
         return self._names
 
     def _get_mapping(self):
         """ Gets the current mapping.
         """
-        if self._object is None:
-            return self.factory._mapping
-
         return self._mapping
 
     def _get_inverse_mapping(self):
         """ Gets the current inverse mapping.
         """
-        if self._object is None:
-            return self.factory._inverse_mapping
-
         return self._inverse_mapping
 
     def rebuild_editor(self):
@@ -117,14 +111,16 @@ def rebuild_editor(self):
         raise NotImplementedError
 
     def values_changed(self):
-        """ Recomputes the cached data based on the underlying enumeration model.
+        """ Recomputes the cached data based on the underlying enumeration model
+            or the values of the factory.
         """
         self._names, self._mapping, self._inverse_mapping = enum_values_changed(
-            self._value()
+            self._value(), self.string_value
         )
 
     def _values_changed(self):
-        """ Handles the underlying object model's enumeration set being changed.
+        """ Handles the underlying object model's enumeration set or factory's
+            values being changed.
         """
         self.values_changed()
         self.rebuild_editor()
@@ -138,7 +134,7 @@ def dispose(self):
             )
         else:
             self.factory.on_trait_change(
-                self.rebuild_editor, "values_modified", remove=True
+                self._values_changed, "values", remove=True
             )
 
         super(BaseEditor, self).dispose()
diff --git a/traitsui/wx/helper.py b/traitsui/wx/helper.py
index aded386cf..53bc1d5ea 100644
--- a/traitsui/wx/helper.py
+++ b/traitsui/wx/helper.py
@@ -266,41 +266,6 @@ def top_level_window_for(control):
     return control
 
 
-def enum_values_changed(values):
-    """ Recomputes the mappings for a new set of enumeration values.
-    """
-
-    if isinstance(values, dict):
-        data = [(str(v), n) for n, v in values.items()]
-        if len(data) > 0:
-            data.sort(key=itemgetter(0))
-            col = data[0][0].find(":") + 1
-            if col > 0:
-                data = [(n[col:], v) for n, v in data]
-    elif not isinstance(values, SequenceTypes):
-        handler = values
-        if isinstance(handler, CTrait):
-            handler = handler.handler
-        if not isinstance(handler, BaseTraitHandler):
-            raise TraitError("Invalid value for 'values' specified")
-        if handler.is_mapped:
-            data = [(str(n), n) for n in handler.map.keys()]
-            data.sort(key=itemgetter(0))
-        else:
-            data = [(str(v), v) for v in handler.values]
-    else:
-        data = [(str(v), v) for v in values]
-
-    names = [x[0] for x in data]
-    mapping = {}
-    inverse_mapping = {}
-    for name, value in data:
-        mapping[name] = value
-        inverse_mapping[value] = name
-
-    return (names, mapping, inverse_mapping)
-
-
 def disconnect(control, *events):
     """ Disconnects a wx event handle from its associated control.
     """
@@ -687,4 +652,4 @@ def _erase_background(self, event):
 
     def Destroy(self):
         self.Unbind(wx.EVT_ERASE_BACKGROUND)
-        super().Destroy()
\ No newline at end of file
+        super().Destroy()
diff --git a/traitsui/wx/image_enum_editor.py b/traitsui/wx/image_enum_editor.py
index 91496a1a3..220281729 100644
--- a/traitsui/wx/image_enum_editor.py
+++ b/traitsui/wx/image_enum_editor.py
@@ -30,12 +30,16 @@
 
 from .editor import Editor
 
+from .enum_editor import BaseEditor as BaseEnumEditor
+
 from .helper import bitmap_cache, position_window, TraitsUIPanel
 
 from .constants import WindowColor
 
 from .image_control import ImageControl
 
+from traitsui.wx import toolkit
+
 # -------------------------------------------------------------------------
 #  'ReadonlyEditor' class:
 # -------------------------------------------------------------------------
@@ -97,7 +101,7 @@ def popup_editor(self, control):
         ImageEnumDialog(self)
 
 
-class CustomEditor(Editor):
+class CustomEditor(BaseEnumEditor):
     """ Custom style of image enumeration editor, which displays a grid of
     ImageControls. The user can click an image to select the corresponding
     value.
@@ -113,13 +117,23 @@ def init(self, parent):
         """ Finishes initializing the editor by creating the underlying toolkit
             widget.
         """
-        self._create_image_grid(parent)
+        super(CustomEditor, self).init(parent)
+
+        # Create the panel to hold the ImageControl buttons:
+        self.control = TraitsUIPanel(parent, -1)
+        self._create_image_grid()
 
-    def _create_image_grid(self, parent):
+    def rebuild_editor(self):
+        # Clear any existing content:
+        self.control.SetSizer(None)
+        toolkit.destroy_children(self.control)
+
+        self._create_image_grid()
+
+    def _create_image_grid(self):
         """ Populates a specified window with a grid of image buttons.
         """
-        # Create the panel to hold the ImageControl buttons:
-        self.control = panel = TraitsUIPanel(parent, -1)
+        panel = self.control
 
         # Create the main sizer:
         if self.factory.cols > 1:
@@ -129,10 +143,9 @@ def _create_image_grid(self, parent):
 
         # Add the set of all possible choices:
         factory = self.factory
-        mapping = factory._mapping
         cur_value = self.value
-        for name in self.factory._names:
-            value = mapping[name]
+        for name in self.names:
+            value = self.mapping[name]
             control = ImageControl(
                 panel,
                 bitmap_cache(
diff --git a/traitsui/wx/set_editor.py b/traitsui/wx/set_editor.py
index 883a896ea..a10095990 100644
--- a/traitsui/wx/set_editor.py
+++ b/traitsui/wx/set_editor.py
@@ -31,9 +31,11 @@
 # traitsui.editors.set_editor file.
 from traitsui.editors.set_editor import ToolkitEditorFactory
 
+from traitsui.helper import enum_values_changed
+
 from .editor import Editor
 
-from .helper import enum_values_changed, TraitsUIPanel
+from .helper import TraitsUIPanel
 
 
 # -------------------------------------------------------------------------
@@ -81,8 +83,10 @@ def init(self, parent):
                 self._values_changed, self._name, dispatch="ui"
             )
         else:
+            self._value = lambda: self.factory.values
+            self.values_changed()
             factory.on_trait_change(
-                self.update_editor, "values_modified", dispatch="ui"
+                self._values_changed, "values", dispatch="ui"
             )
 
         self.control = panel = TraitsUIPanel(parent, -1)
@@ -139,25 +143,16 @@ def init(self, parent):
     def _get_names(self):
         """ Gets the current set of enumeration names.
         """
-        if self._object is None:
-            return self.factory._names
-
         return self._names
 
     def _get_mapping(self):
         """ Gets the current mapping.
         """
-        if self._object is None:
-            return self.factory._mapping
-
         return self._mapping
 
     def _get_inverse_mapping(self):
         """ Gets the current inverse mapping.
         """
-        if self._object is None:
-            return self.factory._inverse_mapping
-
         return self._inverse_mapping
 
     def _create_listbox(self, parent, sizer, handler1, handler2, title):
@@ -197,14 +192,16 @@ def _create_button(self, label, parent, sizer, space_before, handler):
         return button
 
     def values_changed(self):
-        """ Recomputes the cached data based on the underlying enumeration model.
+        """ Recomputes the cached data based on the underlying enumeration model
+            or the values of the factory.
         """
         self._names, self._mapping, self._inverse_mapping = enum_values_changed(
-            self._value()
+            self._value(), self.string_value
         )
 
     def _values_changed(self):
-        """ Handles the underlying object model's enumeration set being changed.
+        """ Handles the underlying object model's enumeration set or factory's
+            values being changed.
         """
         self.values_changed()
         self.update_editor()
@@ -287,7 +284,7 @@ def dispose(self):
             )
         else:
             self.factory.on_trait_change(
-                self.update_editor, "values_modified", remove=True
+                self._values_changed, "values", remove=True
             )
 
         self.context_object.on_trait_change(