diff --git a/lib/matplotlib/colorbar.py b/lib/matplotlib/colorbar.py
index e812550c46fd..e5b02701df96 100644
--- a/lib/matplotlib/colorbar.py
+++ b/lib/matplotlib/colorbar.py
@@ -1149,16 +1149,21 @@ def _mesh(self):
             return (Y, X, extendlen)
 
     def _forward_boundaries(self, x):
+        # map boundaries equally between 0 and 1...
         b = self._boundaries
-        y = np.interp(x, b, np.linspace(0, b[-1], len(b)))
+        y = np.interp(x, b, np.linspace(0, 1, len(b)))
+        # the following avoids ticks in the extends:
         eps = (b[-1] - b[0]) * 1e-6
+        # map these _well_ out of bounds to keep any ticks out
+        # of the extends region...
         y[x < b[0]-eps] = -1
         y[x > b[-1]+eps] = 2
         return y
 
     def _inverse_boundaries(self, x):
+        # invert the above...
         b = self._boundaries
-        return np.interp(x, np.linspace(0, b[-1], len(b)), b)
+        return np.interp(x, np.linspace(0, 1, len(b)), b)
 
     def _reset_locator_formatter_scale(self):
         """
diff --git a/lib/matplotlib/tests/test_colorbar.py b/lib/matplotlib/tests/test_colorbar.py
index b85726d9146b..8ca161284cb0 100644
--- a/lib/matplotlib/tests/test_colorbar.py
+++ b/lib/matplotlib/tests/test_colorbar.py
@@ -873,3 +873,32 @@ def test_proportional_colorbars():
             CS3 = axs[i, j].contourf(X, Y, Z, levels, cmap=cmap, norm=norm,
                                      extend=extends[i])
             fig.colorbar(CS3, spacing=spacings[j], ax=axs[i, j])
+
+
+def test_negative_boundarynorm():
+    fig, ax = plt.subplots(figsize=(1, 3))
+    cmap = plt.get_cmap("viridis")
+
+    clevs = np.arange(-94, -85)
+    norm = BoundaryNorm(clevs, cmap.N)
+    cb = fig.colorbar(cm.ScalarMappable(cmap=cmap, norm=norm), cax=ax)
+    np.testing.assert_allclose(cb.ax.get_ylim(), [clevs[0], clevs[-1]])
+    np.testing.assert_allclose(cb.ax.get_yticks(), clevs)
+
+    clevs = np.arange(85, 94)
+    norm = BoundaryNorm(clevs, cmap.N)
+    cb = fig.colorbar(cm.ScalarMappable(cmap=cmap, norm=norm), cax=ax)
+    np.testing.assert_allclose(cb.ax.get_ylim(), [clevs[0], clevs[-1]])
+    np.testing.assert_allclose(cb.ax.get_yticks(), clevs)
+
+    clevs = np.arange(-3, 3)
+    norm = BoundaryNorm(clevs, cmap.N)
+    cb = fig.colorbar(cm.ScalarMappable(cmap=cmap, norm=norm), cax=ax)
+    np.testing.assert_allclose(cb.ax.get_ylim(), [clevs[0], clevs[-1]])
+    np.testing.assert_allclose(cb.ax.get_yticks(), clevs)
+
+    clevs = np.arange(-8, 1)
+    norm = BoundaryNorm(clevs, cmap.N)
+    cb = fig.colorbar(cm.ScalarMappable(cmap=cmap, norm=norm), cax=ax)
+    np.testing.assert_allclose(cb.ax.get_ylim(), [clevs[0], clevs[-1]])
+    np.testing.assert_allclose(cb.ax.get_yticks(), clevs)
diff --git a/lib/matplotlib/tests/test_contour.py b/lib/matplotlib/tests/test_contour.py
index 6396105f12ec..5d887416a459 100644
--- a/lib/matplotlib/tests/test_contour.py
+++ b/lib/matplotlib/tests/test_contour.py
@@ -305,8 +305,12 @@ def test_clabel_zorder(use_clabeltext, contour_zorder, clabel_zorder):
         assert clabel.get_zorder() == expected_clabel_zorder
 
 
+# tol because ticks happen to fall on pixel boundaries so small
+# floating point changes in tick location flip which pixel gets
+# the tick.
 @image_comparison(['contour_log_extension.png'],
-                  remove_text=True, style='mpl20')
+                  remove_text=True, style='mpl20',
+                  tol=1.444)
 def test_contourf_log_extension():
     # Remove this line when this test image is regenerated.
     plt.rcParams['pcolormesh.snap'] = False