diff --git a/scripts/Engineering/gui/engineering_diffraction/tabs/fitting/plotting/plot_model.py b/scripts/Engineering/gui/engineering_diffraction/tabs/fitting/plotting/plot_model.py
index 8f30433890c6681a8c40d6a2dff66958bb6aca18..4f8ae77586e94c674b77c99c810cedbfe011f787 100644
--- a/scripts/Engineering/gui/engineering_diffraction/tabs/fitting/plotting/plot_model.py
+++ b/scripts/Engineering/gui/engineering_diffraction/tabs/fitting/plotting/plot_model.py
@@ -8,14 +8,14 @@
 
 class FittingPlotModel(object):
     def __init__(self):
-        self.plotted_workspaces = []
+        self.plotted_workspaces = set()
 
     def get_plotted_workspaces(self):
         return self.plotted_workspaces
 
     def add_workspace_to_plot(self, ws, ax, plot_kwargs):
         ax.plot(ws, **plot_kwargs)
-        self.plotted_workspaces.append(ws)
+        self.plotted_workspaces.add(ws)
 
     def remove_workspace_from_plot(self, ws, ax):
         if ws in self.plotted_workspaces:
@@ -27,7 +27,5 @@ class FittingPlotModel(object):
         ax.remove_workspace_artists(ws)
 
     def remove_all_workspaces_from_plot(self, ax):
-        for ws in self.plotted_workspaces:
-            self._remove_workspace_from_plot(ws, ax)
-        # Should already be empty, but just to be sure.
+        ax.cla()
         self.plotted_workspaces.clear()
diff --git a/scripts/Engineering/gui/engineering_diffraction/tabs/fitting/plotting/test/test_plot_model.py b/scripts/Engineering/gui/engineering_diffraction/tabs/fitting/plotting/test/test_plot_model.py
index fdfc77009ad4a6f1a3d5b7cf87566df24fa07447..32c7aa275bce61ea993bf7b29365c8a42fa89711 100644
--- a/scripts/Engineering/gui/engineering_diffraction/tabs/fitting/plotting/test/test_plot_model.py
+++ b/scripts/Engineering/gui/engineering_diffraction/tabs/fitting/plotting/test/test_plot_model.py
@@ -19,42 +19,40 @@ class FittingPlotModelTest(unittest.TestCase):
         self.model = plot_model.FittingPlotModel()
 
     def test_adding_workspace_to_plot(self):
-        self.assertEqual([], self.model.plotted_workspaces)
+        self.assertEqual(set(), self.model.plotted_workspaces)
         ax = mock.MagicMock()
 
         self.model.add_workspace_to_plot("mocked_ws", ax, {"linestyle": "x"})
 
-        self.assertEqual(["mocked_ws"], self.model.plotted_workspaces)
+        self.assertEqual({"mocked_ws"}, self.model.plotted_workspaces)
         ax.plot.assert_called_once_with("mocked_ws", linestyle="x")
 
     def test_removing_single_tracked_workspace_from_plot(self):
-        self.model.plotted_workspaces.append("mocked_ws")
+        self.model.plotted_workspaces.add("mocked_ws")
         ax = mock.MagicMock()
 
         self.model.remove_workspace_from_plot("mocked_ws", ax)
 
-        self.assertEqual([], self.model.plotted_workspaces)
+        self.assertEqual(set(), self.model.plotted_workspaces)
         ax.remove_workspace_artists.assert_called_once_with("mocked_ws")
 
     def test_removing_not_tracked_workspace_from_plot(self):
-        self.model.plotted_workspaces.append("mocked_ws")
+        self.model.plotted_workspaces.add("mocked_ws")
         ax = mock.MagicMock()
 
         self.model.remove_workspace_from_plot("whatever", ax)
 
-        self.assertEqual(["mocked_ws"], self.model.plotted_workspaces)
+        self.assertEqual({"mocked_ws"}, self.model.plotted_workspaces)
         ax.remove_workspace_artists.assert_not_called()
 
     def test_removing_all_workspaces_from_plot(self):
-        self.model.plotted_workspaces.extend(["mocked_ws", "mock_ws_2"])
+        self.model.plotted_workspaces.update({"mocked_ws", "mock_ws_2"})
         ax = mock.MagicMock()
 
         self.model.remove_all_workspaces_from_plot(ax)
 
-        self.assertEqual([], self.model.plotted_workspaces)
-        ax.remove_workspace_artists.assert_any_call("mocked_ws")
-        ax.remove_workspace_artists.assert_any_call("mock_ws_2")
-        self.assertEqual(2, ax.remove_workspace_artists.call_count)
+        self.assertEqual(set(), self.model.plotted_workspaces)
+        self.assertEqual(1, ax.cla.call_count)
 
 
 if __name__ == '__main__':