diff --git a/glue/core/coordinates.py b/glue/core/coordinates.py
index 63f280daa..7eac0d11a 100644
--- a/glue/core/coordinates.py
+++ b/glue/core/coordinates.py
@@ -209,6 +209,10 @@ def __setgluestate__(cls, rec, context):
                    units=rec['units'],
                    labels=rec['labels'])
 
+    @property
+    def axis_correlation_matrix(self):
+        return self._matrix[:-1, :-1] != 0
+
 
 # Kept for backward-compatibility
 WCSCoordinates = WCS
diff --git a/glue/viewers/histogram/tests/test_python_export.py b/glue/viewers/histogram/tests/test_python_export.py
new file mode 100644
index 000000000..07cb695ae
--- /dev/null
+++ b/glue/viewers/histogram/tests/test_python_export.py
@@ -0,0 +1,61 @@
+from astropy.utils import NumpyRNGContext
+
+from glue.core import Data, DataCollection
+from glue.core.application_base import Application
+from glue.viewers.histogram.viewer import SimpleHistogramViewer
+from glue.viewers.matplotlib.tests.test_python_export import BaseTestExportPython, random_with_nan
+
+
+class TestExportPython(BaseTestExportPython):
+
+    def setup_method(self, method):
+
+        with NumpyRNGContext(12345):
+            self.data = Data(**dict((name, random_with_nan(100, nan_index=idx + 1)) for idx, name in enumerate('abcdefgh')))
+        self.data_collection = DataCollection([self.data])
+        self.app = Application(self.data_collection)
+        self.viewer = self.app.new_data_viewer(SimpleHistogramViewer)
+        self.viewer.add_data(self.data)
+        self.viewer.state.x_att = self.data.id['a']
+
+    def teardown_method(self, method):
+        self.viewer = None
+        self.app = None
+
+    def test_simple(self, tmpdir):
+        self.assert_same(tmpdir)
+
+    def test_simple_visual(self, tmpdir):
+        self.viewer.state.layers[0].color = 'blue'
+        self.viewer.state.layers[0].alpha = 0.5
+        self.assert_same(tmpdir)
+
+    def test_simple_visual_legend(self, tmpdir):
+        self.viewer.state.legend.visible = True
+        self.viewer.state.layers[0].color = 'blue'
+        self.viewer.state.layers[0].alpha = 0.5
+        self.assert_same(tmpdir)
+
+    def test_cumulative(self, tmpdir):
+        self.viewer.state.cumulative = True
+        self.assert_same(tmpdir)
+
+    def test_normalize(self, tmpdir):
+        self.viewer.state.normalize = True
+        self.assert_same(tmpdir)
+
+    def test_subset(self, tmpdir):
+        self.data_collection.new_subset_group('mysubset', self.data.id['a'] > 0.5)
+        self.assert_same(tmpdir)
+
+    def test_subset_legend(self, tmpdir):
+        self.viewer.state.legend.visible = True
+        self.data_collection.new_subset_group('mysubset', self.data.id['a'] > 0.5)
+        self.assert_same(tmpdir)
+
+    def test_empty(self, tmpdir):
+        self.viewer.state.x_min = 10
+        self.viewer.state.x_max = 11
+        self.viewer.state.hist_x_min = 10
+        self.viewer.state.hist_x_max = 11
+        self.assert_same(tmpdir)
diff --git a/glue/viewers/image/state.py b/glue/viewers/image/state.py
index 9258646b9..59f5db95e 100644
--- a/glue/viewers/image/state.py
+++ b/glue/viewers/image/state.py
@@ -257,7 +257,7 @@ def _on_yatt_change(self, *args):
                 self.y_att_world = self.y_att
 
     @defer_draw
-    def _on_xatt_world_change(self, *args):
+    def _on_xatt_world_change(self, *args, forced=False):
 
         if self.x_att_world is not None:
 
@@ -279,8 +279,11 @@ def _on_xatt_world_change(self, *args):
                 else:
                     self.x_att = self.x_att_world
 
+                if not forced:
+                    self._on_yatt_world_change(forced=True)
+
     @defer_draw
-    def _on_yatt_world_change(self, *args):
+    def _on_yatt_world_change(self, *args, forced=False):
 
         if self.y_att_world is not None:
 
@@ -302,6 +305,9 @@ def _on_yatt_world_change(self, *args):
                 else:
                     self.y_att = self.y_att_world
 
+            if not forced:
+                self._on_xatt_world_change(forced=True)
+
     def _set_reference_data(self):
         if self.reference_data is None:
             for layer in self.layers:
diff --git a/glue/viewers/image/tests/test_python_export.py b/glue/viewers/image/tests/test_python_export.py
new file mode 100644
index 000000000..fff360a5e
--- /dev/null
+++ b/glue/viewers/image/tests/test_python_export.py
@@ -0,0 +1,124 @@
+import pytest
+import numpy as np
+import matplotlib.pyplot as plt
+from astropy.utils import NumpyRNGContext
+from astropy.wcs import WCS
+
+from glue.core import Data, DataCollection
+from glue.core.coordinates import AffineCoordinates
+from glue.core.application_base import Application
+from glue.viewers.image.viewer import SimpleImageViewer
+from glue.viewers.matplotlib.tests.test_python_export import BaseTestExportPython
+
+
+class TestExportPython(BaseTestExportPython):
+
+    def setup_method(self, method):
+
+        with NumpyRNGContext(12345):
+            self.data = Data(cube=np.random.random((30, 50, 20)))
+        # Create data versions with WCS and affine coordinates
+        matrix = np.array([[2, 0, 0, -1], [0, 2, 1, 2], [0, 3, 1, -2], [0, 0, 0, 1]])
+        affine = AffineCoordinates(matrix, units=['Mm', 'Mm', 'km'], labels=['xw', 'yw', 'zw'])
+
+        self.data_wcs = Data(label='cube', cube=self.data['cube'], coords=WCS(naxis=3))
+        self.data_affine = Data(label='cube', cube=self.data['cube'], coords=affine)
+        self.data_collection = DataCollection([self.data, self.data_wcs, self.data_affine])
+        self.app = Application(self.data_collection)
+        self.viewer = self.app.new_data_viewer(SimpleImageViewer)
+        self.viewer.add_data(self.data)
+        # FIXME: On some platforms, using an integer label size
+        # causes some of the labels to be non-deterministically
+        # shifted by one pixel, so we pick a non-round font size
+        # to avoid this.
+        self.viewer.state.x_ticklabel_size = 8.21334111
+        self.viewer.state.y_ticklabel_size = 8.21334111
+
+    def teardown_method(self, method):
+        self.viewer = None
+        self.app = None
+
+    def assert_same(self, tmpdir, tol=0.1):
+        BaseTestExportPython.assert_same(self, tmpdir, tol=tol)
+
+    def viewer_load(self, coords):
+        if coords is not None:
+            self.viewer.add_data(getattr(self, f'data_{coords}'))
+            self.viewer.remove_data(self.data)
+
+    @pytest.mark.parametrize('coords', [None, 'wcs', 'affine'])
+    def test_simple(self, tmpdir, coords):
+        self.viewer_load(coords)
+        self.assert_same(tmpdir)
+
+    @pytest.mark.parametrize('coords', [None, 'wcs', 'affine'])
+    def test_simple_legend(self, tmpdir, coords):
+        self.viewer_load(coords)
+        self.viewer.state.show_legend = True
+        self.assert_same(tmpdir)
+
+    @pytest.mark.parametrize('coords', [None, 'wcs', 'affine'])
+    def test_simple_att(self, tmpdir, coords):
+        self.viewer_load(coords)
+        self.viewer.state.x_att = self.viewer.state.reference_data.pixel_component_ids[1]
+        self.viewer.state.y_att = self.viewer.state.reference_data.pixel_component_ids[0]
+        if coords == 'affine':
+            pytest.xfail('Known issue with axis label rendering')
+        self.assert_same(tmpdir)
+
+    @pytest.mark.parametrize('coords', [None, 'wcs', 'affine'])
+    def test_simple_visual(self, tmpdir, coords):
+        self.viewer_load(coords)
+        self.viewer.state.legend.visible = True
+        self.viewer.state.layers[0].cmap = plt.cm.RdBu
+        self.viewer.state.layers[0].v_min = 0.2
+        self.viewer.state.layers[0].v_max = 0.8
+        self.viewer.state.layers[0].stretch = 'sqrt'
+        self.viewer.state.layers[0].stretch = 'sqrt'
+        self.viewer.state.layers[0].contrast = 0.9
+        self.viewer.state.layers[0].bias = 0.6
+        self.assert_same(tmpdir)
+
+    @pytest.mark.parametrize('coords', [None, 'wcs', 'affine'])
+    def test_slice(self, tmpdir, coords):
+        self.viewer_load(coords)
+        self.viewer.state.x_att = self.viewer.state.reference_data.pixel_component_ids[1]
+        self.viewer.state.y_att = self.viewer.state.reference_data.pixel_component_ids[0]
+        self.viewer.state.slices = (2, 3, 4)
+        if coords == 'affine':
+            pytest.xfail('Known issue with axis label rendering')
+        self.assert_same(tmpdir)
+
+    @pytest.mark.parametrize('coords', [None, 'wcs', 'affine'])
+    def test_aspect(self, tmpdir, coords):
+        self.viewer_load(coords)
+        self.viewer.state.aspect = 'auto'
+        self.assert_same(tmpdir)
+
+    @pytest.mark.parametrize('coords', [None, 'wcs', 'affine'])
+    def test_subset(self, tmpdir, coords):
+        self.viewer_load(coords)
+        self.data_collection.new_subset_group('mysubset', self.data.id['cube'] > 0.5)
+        self.assert_same(tmpdir)
+
+    @pytest.mark.parametrize('coords', [None, 'wcs', 'affine'])
+    def test_subset_legend(self, tmpdir, coords):
+        self.viewer_load(coords)
+        self.data_collection.new_subset_group('mysubset',
+                                              self.viewer.state.reference_data.id['cube'] > 0.5)
+        self.viewer.state.legend.visible = True
+        self.assert_same(tmpdir, tol=0.15)  # transparency and such
+
+    @pytest.mark.parametrize('coords', [None, 'wcs', 'affine'])
+    def test_subset_slice(self, tmpdir, coords):
+        self.viewer_load(coords)
+        self.data_collection.new_subset_group('mysubset', self.data.id['cube'] > 0.5)
+        self.test_slice(tmpdir, coords)
+
+    @pytest.mark.parametrize('coords', [None, 'wcs', 'affine'])
+    def test_subset_transposed(self, tmpdir, coords):
+        self.viewer_load(coords)
+        self.data_collection.new_subset_group('mysubset', self.data.id['cube'] > 0.5)
+        self.viewer.state.x_att = self.data.pixel_component_ids[0]
+        self.viewer.state.y_att = self.data.pixel_component_ids[1]
+        self.assert_same(tmpdir)
diff --git a/glue/viewers/matplotlib/tests/test_python_export.py b/glue/viewers/matplotlib/tests/test_python_export.py
new file mode 100644
index 000000000..24213c8f2
--- /dev/null
+++ b/glue/viewers/matplotlib/tests/test_python_export.py
@@ -0,0 +1,62 @@
+import os
+import sys
+import pytest
+import subprocess
+
+from glue.config import settings
+
+import numpy as np
+
+from matplotlib.testing.compare import compare_images
+
+__all__ = ['random_with_nan', 'BaseTestExportPython']
+
+
+def random_with_nan(nsamples, nan_index):
+    x = np.random.random(nsamples)
+    x[nan_index] = np.nan
+    return x
+
+
+class BaseTestExportPython:
+
+    def assert_same(self, tmpdir, tol=0.1):
+
+        os.chdir(tmpdir.strpath)
+
+        expected = tmpdir.join('expected.png').strpath
+        script = tmpdir.join('actual.py').strpath
+        actual = tmpdir.join('glue_plot.png').strpath
+
+        self.viewer.axes.figure.savefig(expected)
+
+        self.viewer.export_as_script(script)
+        subprocess.call([sys.executable, script])
+
+        msg = compare_images(expected, actual, tol=tol)
+
+        if msg:
+
+            from base64 import b64encode
+
+            print("SCRIPT:")
+            with open(script, 'r') as f:
+                print(f.read())
+
+            print("EXPECTED:")
+            with open(expected, 'rb') as f:
+                print(b64encode(f.read()).decode())
+
+            print("ACTUAL:")
+            with open(actual, 'rb') as f:
+                print(b64encode(f.read()).decode())
+
+            pytest.fail(msg, pytrace=False)
+
+    def test_color_settings(self, tmpdir):
+        settings.FOREGROUND_COLOR = '#a51d2d'
+        settings.BACKGROUND_COLOR = '#99c1f1'
+        self.viewer._update_appearance_from_settings()
+        self.assert_same(tmpdir)
+        settings.reset_defaults()
+        self.viewer._update_appearance_from_settings()
diff --git a/glue/viewers/profile/tests/test_python_export.py b/glue/viewers/profile/tests/test_python_export.py
new file mode 100644
index 000000000..589a41288
--- /dev/null
+++ b/glue/viewers/profile/tests/test_python_export.py
@@ -0,0 +1,87 @@
+from astropy.utils import NumpyRNGContext
+
+from glue.core import Data, DataCollection
+from glue.core.application_base import Application
+from glue.viewers.profile.viewer import SimpleProfileViewer
+from glue.viewers.matplotlib.tests.test_python_export import BaseTestExportPython, random_with_nan
+from glue.viewers.profile.tests.test_state import SimpleCoordinates
+
+
+class TestExportPython(BaseTestExportPython):
+
+    def setup_method(self, method):
+
+        self.data = Data(label='d1')
+        self.data.coords = SimpleCoordinates()
+        with NumpyRNGContext(12345):
+            self.data['x'] = random_with_nan(48, 5).reshape((6, 4, 2))
+            self.data['y'] = random_with_nan(48, 12).reshape((6, 4, 2))
+        self.data_collection = DataCollection([self.data])
+        self.app = Application(self.data_collection)
+        self.viewer = self.app.new_data_viewer(SimpleProfileViewer)
+        self.viewer.add_data(self.data)
+        # Make legend location deterministic
+        self.viewer.state.legend.location = 'lower left'
+
+    def teardown_method(self, method):
+        self.viewer = None
+        self.app = None
+
+    def test_simple(self, tmpdir):
+        self.assert_same(tmpdir)
+
+    def test_simple_legend(self, tmpdir):
+        self.viewer.state.legend.visible = True
+        self.assert_same(tmpdir)
+
+    def test_color(self, tmpdir):
+        self.viewer.state.layers[0].color = '#ac0567'
+        self.assert_same(tmpdir)
+
+    def test_linewidth(self, tmpdir):
+        self.viewer.state.layers[0].linewidth = 7.25
+        self.assert_same(tmpdir)
+
+    def test_max(self, tmpdir):
+        self.viewer.state.function = 'maximum'
+        self.assert_same(tmpdir)
+
+    def test_min(self, tmpdir):
+        self.viewer.state.function = 'minimum'
+        self.assert_same(tmpdir)
+
+    def test_mean(self, tmpdir):
+        self.viewer.state.function = 'mean'
+        self.assert_same(tmpdir)
+
+    def test_median(self, tmpdir):
+        self.viewer.state.function = 'median'
+        self.assert_same(tmpdir)
+
+    def test_sum(self, tmpdir):
+        self.viewer.state.function = 'sum'
+        self.assert_same(tmpdir)
+
+    def test_normalization(self, tmpdir):
+        self.viewer.state.normalize = True
+        self.assert_same(tmpdir)
+
+    def test_subset(self, tmpdir):
+        self.viewer.state.function = 'mean'
+        self.data_collection.new_subset_group('mysubset', self.data.id['x'] > 0.25)
+        self.assert_same(tmpdir)
+
+    def test_subset_legend(self, tmpdir):
+        self.viewer.state.legend.visible = True
+        self.viewer.state.function = 'mean'
+        self.viewer.state.layers[0].linewidth = 7.25
+        self.data_collection.new_subset_group('mysubset', self.data.id['x'] > 0.25)
+        self.assert_same(tmpdir)
+
+    def test_xatt(self, tmpdir):
+        self.viewer.x_att = self.data.pixel_component_ids[1]
+        self.assert_same(tmpdir)
+
+    def test_profile_att(self, tmpdir):
+        self.viewer.layers[0].state.attribute = self.data.id['y']
+        self.assert_same(tmpdir)
diff --git a/glue/viewers/scatter/tests/test_python_export.py b/glue/viewers/scatter/tests/test_python_export.py
new file mode 100644
index 000000000..c89d4919a
--- /dev/null
+++ b/glue/viewers/scatter/tests/test_python_export.py
@@ -0,0 +1,299 @@
+from itertools import product
+
+import numpy as np
+import matplotlib.pyplot as plt
+from astropy.utils import NumpyRNGContext
+
+from glue.core import Data, DataCollection
+from glue.core.application_base import Application
+from glue.viewers.scatter.viewer import SimpleScatterViewer
+from glue.viewers.matplotlib.tests.test_python_export import BaseTestExportPython, random_with_nan
+
+
+class TestExportPython(BaseTestExportPython):
+
+    def setup_method(self, method):
+
+        with NumpyRNGContext(12345):
+            self.data = Data(**dict((name, random_with_nan(100, nan_index=idx + 1)) for idx, name in enumerate('abcdefgh')))
+        self.data['angle'] = np.random.uniform(0, 360, 100)
+        self.data_collection = DataCollection([self.data])
+        self.app = Application(self.data_collection)
+        self.viewer = self.app.new_data_viewer(SimpleScatterViewer)
+        self.viewer.add_data(self.data)
+        self.viewer.state.x_att = self.data.id['a']
+        self.viewer.state.y_att = self.data.id['b']
+
+    def teardown_method(self, method):
+        self.viewer = None
+        self.app = None
+
+    def test_simple(self, tmpdir):
+        self.assert_same(tmpdir)
+
+    def test_simple_legend(self, tmpdir):
+        self.viewer.state.legend.visible = True
+        self.assert_same(tmpdir)
+
+    def test_simple_nofill(self, tmpdir):
+        self.viewer.state.layers[0].fill = False
+        self.viewer.state.layers[0].size_scaling = 10
+        self.assert_same(tmpdir)
+
+    def test_simple_visual(self, tmpdir):
+        self.viewer.state.layers[0].color = 'blue'
+        self.viewer.state.layers[0].markersize = 30
+        self.viewer.state.layers[0].alpha = 0.5
+        self.assert_same(tmpdir)
+
+    def test_simple_visual_legend(self, tmpdir):
+        self.viewer.state.legend.visible = True
+        self.viewer.state.layers[0].color = 'blue'
+        self.viewer.state.layers[0].markersize = 30
+        self.viewer.state.layers[0].alpha = 0.5
+        self.assert_same(tmpdir)
+
+    def test_cmap_mode(self, tmpdir):
+        self.viewer.state.layers[0].cmap_mode = 'Linear'
+        self.viewer.state.layers[0].cmap_att = self.data.id['c']
+        self.viewer.state.layers[0].cmap = plt.cm.BuGn
+        self.viewer.state.layers[0].cmap_vmin = 0.2
+        self.viewer.state.layers[0].cmap_vmax = 0.7
+        self.viewer.state.layers[0].alpha = 0.8
+        self.assert_same(tmpdir)
+
+    def test_cmap_mode_nofill(self, tmpdir):
+        self.viewer.state.layers[0].fill = False
+        self.test_cmap_mode(tmpdir)
+
+    def test_size_mode(self, tmpdir):
+        self.viewer.state.layers[0].size_mode = 'Linear'
+        self.viewer.state.layers[0].size_att = self.data.id['d']
+        self.viewer.state.layers[0].size_vmin = 0.1
+        self.viewer.state.layers[0].size_vmax = 0.8
+        self.viewer.state.layers[0].size_scaling = 0.4
+        self.viewer.state.layers[0].alpha = 0.7
+        self.assert_same(tmpdir)
+
+    def test_size_mode_legend(self, tmpdir):
+        self.viewer.state.legend.visible = True
+        self.viewer.state.layers[0].size_mode = 'Linear'
+        self.viewer.state.layers[0].size_att = self.data.id['d']
+        self.viewer.state.layers[0].size_vmin = 0.1
+        self.viewer.state.layers[0].size_vmax = 0.8
+        self.viewer.state.layers[0].size_scaling = 0.4
+        self.viewer.state.layers[0].alpha = 0.7
+        self.assert_same(tmpdir)
+
+    def test_size_mode_nofill(self, tmpdir):
+        self.viewer.state.layers[0].fill = False
+        self.test_size_mode(tmpdir)
+
+    def test_line(self, tmpdir):
+        self.viewer.state.layers[0].line_visible = True
+        self.viewer.state.layers[0].linewidth = 10
+        self.viewer.state.layers[0].linestype = 'dashed'
+        self.viewer.state.layers[0].color = 'orange'
+        self.viewer.state.layers[0].alpha = 0.7
+        self.viewer.state.layers[0].markersize = 100
+        self.assert_same(tmpdir, tol=5)
+
+    def test_line_cmap(self, tmpdir):
+        self.viewer.state.layers[0].cmap_mode = 'Linear'
+        self.viewer.state.layers[0].cmap_vmin = 0.2
+        self.viewer.state.layers[0].cmap_vmax = 0.7
+        self.viewer.state.layers[0].cmap = plt.cm.BuGn
+        self.test_line(tmpdir)
+
+    def test_errorbarx(self, tmpdir):
+        self.viewer.state.layers[0].xerr_visible = True
+        self.viewer.state.layers[0].xerr_att = self.data.id['e']
+        self.viewer.state.layers[0].color = 'purple'
+        self.viewer.state.layers[0].alpha = 0.5
+        self.assert_same(tmpdir)
+
+    def test_errorbary(self, tmpdir):
+        self.viewer.state.layers[0].yerr_visible = True
+        self.viewer.state.layers[0].yerr_att = self.data.id['f']
+        self.viewer.state.layers[0].color = 'purple'
+        self.viewer.state.layers[0].alpha = 0.5
+        self.assert_same(tmpdir)
+
+    def test_errorbarxy(self, tmpdir):
+        self.viewer.state.layers[0].xerr_visible = True
+        self.viewer.state.layers[0].xerr_att = self.data.id['e']
+        self.viewer.state.layers[0].yerr_visible = True
+        self.viewer.state.layers[0].yerr_att = self.data.id['f']
+        self.viewer.state.layers[0].color = 'purple'
+        self.viewer.state.layers[0].alpha = 0.5
+        self.assert_same(tmpdir)
+
+    def test_errorbarxy_legend(self, tmpdir):
+        self.viewer.state.legend.visible = True
+        self.viewer.state.layers[0].xerr_visible = True
+        self.viewer.state.layers[0].xerr_att = self.data.id['e']
+        self.viewer.state.layers[0].yerr_visible = True
+        self.viewer.state.layers[0].yerr_att = self.data.id['f']
+        self.viewer.state.layers[0].color = 'purple'
+        self.viewer.state.layers[0].alpha = 0.5
+        self.assert_same(tmpdir)
+
+    def test_errorbarxy_cmap(self, tmpdir):
+        self.viewer.state.layers[0].cmap_mode = 'Linear'
+        self.viewer.state.layers[0].cmap_vmin = 0.2
+        self.viewer.state.layers[0].cmap_vmax = 0.7
+        self.viewer.state.layers[0].cmap = plt.cm.BuGn
+        self.test_errorbarxy(tmpdir)
+
+    def _vector_common(self, tmpdir):
+        self.viewer.state.layers[0].vector_visible = True
+        self.viewer.state.layers[0].vy_att = self.data.id['g']
+        self.viewer.state.layers[0].vector_arrowhead = True
+        self.viewer.state.layers[0].vector_origin = 'tail'
+        self.viewer.state.layers[0].vector_scaling = 1.5
+        self.viewer.state.layers[0].color = 'teal'
+        self.viewer.state.layers[0].alpha = 0.9
+        self.assert_same(tmpdir, tol=1)
+
+    def test_vector_cartesian(self, tmpdir):
+        self.viewer.state.layers[0].vector_mode = 'Cartesian'
+        self.viewer.state.layers[0].vx_att = self.data.id['h']
+        self._vector_common(tmpdir)
+
+    def test_vector_polar(self, tmpdir):
+        self.viewer.state.layers[0].vector_mode = 'Polar'
+        self.viewer.state.layers[0].vx_att = self.data.id['angle']
+        self._vector_common(tmpdir)
+
+    def test_vector_cartesian_cmap(self, tmpdir):
+        self.viewer.state.layers[0].cmap_mode = 'Linear'
+        self.viewer.state.layers[0].cmap_vmin = 0.2
+        self.viewer.state.layers[0].cmap_vmax = 0.7
+        self.viewer.state.layers[0].cmap = plt.cm.BuGn
+        self.test_vector_cartesian(tmpdir)
+
+    def test_vector_cartesian_xflip(self, tmpdir):
+        # Regression test for a bug that caused vectors to not be flipped
+        self.viewer.state.layers[0].vector_mode = 'Cartesian'
+        self.viewer.state.layers[0].vx_att = self.data.id['h']
+        self.viewer.state.flip_x()
+        self._vector_common(tmpdir)
+
+    def test_subset(self, tmpdir):
+        self.data_collection.new_subset_group('mysubset', self.data.id['a'] > 0.5)
+        self.assert_same(tmpdir)
+
+    def test_density_map_with_subset(self, tmpdir):
+        self.viewer.state.dpi = 2
+        self.viewer.state.layers[0].density_map = True
+        self.data_collection.new_subset_group('mysubset', self.data.id['a'] > 0.5)
+        self.assert_same(tmpdir)
+
+    def test_density_map_cmap_with_subset(self, tmpdir):
+        self.viewer.state.dpi = 2
+        self.viewer.state.layers[0].density_map = True
+        self.viewer.state.layers[0].cmap_mode = 'Linear'
+        self.viewer.state.layers[0].cmap_vmin = 0.2
+        self.viewer.state.layers[0].cmap_vmax = 0.7
+        self.viewer.state.layers[0].cmap = plt.cm.BuGn
+        self.data_collection.new_subset_group('mysubset', self.data.id['a'] > 0.5)
+        self.assert_same(tmpdir)
+
+    def test_density_map_cmap_with_subset_legend(self, tmpdir):
+        self.viewer.state.legend.visible = True
+        self.viewer.state.dpi = 2
+        self.viewer.state.layers[0].density_map = True
+        self.viewer.state.layers[0].cmap_mode = 'Linear'
+        self.viewer.state.layers[0].cmap_vmin = 0.2
+        self.viewer.state.layers[0].cmap_vmax = 0.7
+        self.viewer.state.layers[0].cmap = plt.cm.BuGn
+        self.data_collection.new_subset_group('mysubset', self.data.id['a'] > 0.5)
+        self.assert_same(tmpdir)
+
+    def test_cmap_mode_change(self, tmpdir):
+        # Regression test for a bug that caused scatter markers to not change
+        # color when going from Linear to Fixed mode
+        self.viewer.state.layers[0].size_mode = 'Linear'
+        self.viewer.state.layers[0].cmap_mode = 'Linear'
+        self.viewer.state.layers[0].cmap_mode = 'Fixed'
+        self.assert_same(tmpdir)
+
+    def test_density_map_change(self, tmpdir):
+        # Regression test for a bug that caused the density map to still
+        # be visible if using color-coding with the density map then
+        # switching to markers.
+        self.viewer.state.layers[0].density_map = True
+        self.viewer.state.layers[0].cmap_mode = 'Linear'
+        self.viewer.state.layers[0].cmap = plt.cm.BuGn
+        self.viewer.state.layers[0].density_map = False
+        self.assert_same(tmpdir)
+
+    def test_simple_polar_plot_degrees(self, tmpdir):
+        self.viewer.state.plot_mode = 'polar'
+        self.viewer.state.angle_unit = 'degrees'
+        self.viewer.state.x_att = self.data.id['c']
+        self.viewer.state.y_att = self.data.id['d']
+        self.assert_same(tmpdir)
+
+    def test_simple_polar_plot_radians(self, tmpdir):
+        self.viewer.state.plot_mode = 'polar'
+        self.viewer.state.angle_unit = 'radians'
+        self.viewer.state.x_att = self.data.id['c']
+        self.viewer.state.y_att = self.data.id['d']
+        self.assert_same(tmpdir)
+
+    def _fullsphere_common_test(self, tmpdir):
+        # Note that all the full-sphere projections have the same bounds,
+        # so we can use the same sets of min/max values
+        x_bounds = self.viewer.state.x_min, self.viewer.state.x_max
+        y_bounds = self.viewer.state.y_min, self.viewer.state.y_max
+        for order in product([True, False], repeat=2):
+            self.viewer.state.x_min, self.viewer.state.x_max = sorted(x_bounds, reverse=order[0])
+            self.viewer.state.y_min, self.viewer.state.y_max = sorted(y_bounds, reverse=order[1])
+            self.viewer.state.plot_mode = 'aitoff'
+            self.viewer.state.x_att = self.data.id['c']
+            self.viewer.state.y_att = self.data.id['d']
+            self.assert_same(tmpdir)
+            self.viewer.state.plot_mode = 'hammer'
+            self.viewer.state.x_att = self.data.id['e']
+            self.viewer.state.y_att = self.data.id['f']
+            self.assert_same(tmpdir)
+            self.viewer.state.plot_mode = 'lambert'
+            self.viewer.state.x_att = self.data.id['g']
+            self.viewer.state.y_att = self.data.id['h']
+            self.assert_same(tmpdir)
+            self.viewer.state.plot_mode = 'mollweide'
+            self.viewer.state.x_att = self.data.id['a']
+            self.viewer.state.y_att = self.data.id['b']
+            self.assert_same(tmpdir)
+
+    def test_full_sphere_degrees(self, tmpdir):
+        self.viewer.state.angle_unit = 'degrees'
+        self._fullsphere_common_test(tmpdir)
+
+    def test_full_sphere_radians(self, tmpdir):
+        self.viewer.state.angle_unit = 'radians'
+        self._fullsphere_common_test(tmpdir)
+
+    def test_cmap_size_noncartesian(self, tmpdir):
+        self.viewer.state.layers[0].size_mode = 'Linear'
+        self.viewer.state.layers[0].cmap_mode = 'Linear'
+        for proj in ['polar', 'aitoff', 'hammer', 'lambert', 'mollweide']:
+            self.viewer.state.plot_mode = proj
+            self.assert_same(tmpdir)
+
+    def test_vectors_noncartesian(self, tmpdir):
+        for proj in ['polar', 'aitoff', 'hammer', 'lambert', 'mollweide']:
+            self.viewer.state.plot_mode = proj
+            self._vector_common(tmpdir)
+
+    def test_errorbarxy_noncartesian(self, tmpdir):
+        self.viewer.state.layers[0].xerr_visible = True
+        self.viewer.state.layers[0].xerr_att = self.data.id['e']
+        self.viewer.state.layers[0].yerr_visible = True
+        self.viewer.state.layers[0].yerr_att = self.data.id['f']
+        self.viewer.state.layers[0].color = 'purple'
+        self.viewer.state.layers[0].alpha = 0.5
+        for proj in ['polar', 'aitoff', 'hammer', 'lambert', 'mollweide']:
+            self.viewer.state.plot_mode = proj
+            self.assert_same(tmpdir)
diff --git a/glue/viewers/scatter/viewer.py b/glue/viewers/scatter/viewer.py
index c986fd706..76289a996 100644
--- a/glue/viewers/scatter/viewer.py
+++ b/glue/viewers/scatter/viewer.py
@@ -1,3 +1,5 @@
+from echo import delay_callback
+
 from glue.core.subset import roi_to_subset_state
 from glue.core.util import update_ticks
 from glue.core.roi_pretransforms import FullSphereLongitudeTransform, ProjectionMplTransform, RadianTransform
@@ -63,13 +65,12 @@ def _update_polar_ticks(self, *args):
     def _update_projection(self, *args):
         self.figure.delaxes(self.axes)
         _, self.axes = init_mpl(self.figure, projection=self.state.plot_mode)
-        self.remove_all_toolbars()
-        self.initialize_toolbar()
         for layer in self.layers:
             layer._set_axes(self.axes)
-            layer.state.vector_mode = 'Cartesian'
-            layer.state._update_points_mode()
-            layer.update()
+            with delay_callback(layer.state, 'vector_mode'):
+                layer.state.vector_mode = 'Cartesian'
+                layer.state._update_points_mode()
+                layer.update()
         self.axes.callbacks.connect('xlim_changed', self.limits_from_mpl)
         self.axes.callbacks.connect('ylim_changed', self.limits_from_mpl)
         self.update_x_axislabel()
@@ -189,6 +190,13 @@ class SimpleScatterViewer(MatplotlibScatterMixin, SimpleMatplotlibViewer):
     _data_artist_cls = ScatterLayerArtist
     _subset_artist_cls = ScatterLayerArtist
 
-    def __init__(self, *args, **kwargs):
-        super().__init__(*args, **kwargs)
+    def __init__(self, session, parent=None, state=None):
+        proj = None if not state or not state.plot_mode else state.plot_mode
+        SimpleMatplotlibViewer.__init__(self, session, parent=parent, state=state, projection=proj)
         MatplotlibScatterMixin.setup_callbacks(self)
+
+    def limits_to_mpl(self, *args):
+        # These projections throw errors if we try to set the limits
+        if self.state.plot_mode in ['aitoff', 'hammer', 'lambert', 'mollweide']:
+            return
+        super().limits_to_mpl(*args)