diff --git a/lib/matplotlib/image.py b/lib/matplotlib/image.py
index de87c2afaa44..f2a7280af553 100644
--- a/lib/matplotlib/image.py
+++ b/lib/matplotlib/image.py
@@ -396,6 +396,28 @@ def _make_image(self, A, in_bbox, out_bbox, clip_bbox, magnification=1.0,
                 # scaled data
                 A_scaled = np.empty(A.shape, dtype=scaled_dtype)
                 A_scaled[:] = A
+                # clip scaled data around norm if necessary.
+                # This is necessary for big numbers at the edge of
+                # float64's ability to represent changes.  Applying
+                # a norm first would be good, but ruins the interpolation
+                # of over numbers.
+                if self.norm.vmin is not None and self.norm.vmax is not None:
+                    dv = (np.float64(self.norm.vmax) -
+                            np.float64(self.norm.vmin))
+                    vmid = self.norm.vmin + dv / 2
+                    newmin = vmid - dv * 1.e7
+                    if newmin < a_min:
+                        newmin = None
+                    else:
+                        a_min = np.float64(newmin)
+                    newmax = vmid + dv * 1.e7
+                    if newmax > a_max:
+                        newmax = None
+                    else:
+                        a_max = np.float64(newmax)
+                    if newmax is not None or newmin is not None:
+                        A_scaled = np.clip(A_scaled, newmin, newmax)
+
                 A_scaled -= a_min
                 # a_min and a_max might be ndarray subclasses so use
                 # asscalar to ensure they are scalars to avoid errors
@@ -614,7 +636,11 @@ def set_data(self, A):
         """
         # check if data is PIL Image without importing Image
         if hasattr(A, 'getpixel'):
-            self._A = pil_to_array(A)
+            if A.mode == 'L':
+                # greyscale image, but our logic assumes rgba:
+                self._A = pil_to_array(A.convert('RGBA'))
+            else:
+                self._A = pil_to_array(A)
         else:
             self._A = cbook.safe_masked_invalid(A, copy=True)
 
diff --git a/lib/matplotlib/tests/baseline_images/test_image/imshow_bignumbers_real.png b/lib/matplotlib/tests/baseline_images/test_image/imshow_bignumbers_real.png
new file mode 100644
index 000000000000..ce3404488ebb
Binary files /dev/null and b/lib/matplotlib/tests/baseline_images/test_image/imshow_bignumbers_real.png differ
diff --git a/lib/matplotlib/tests/test_image.py b/lib/matplotlib/tests/test_image.py
index 16be520e325f..26e3b4a7ea26 100644
--- a/lib/matplotlib/tests/test_image.py
+++ b/lib/matplotlib/tests/test_image.py
@@ -511,6 +511,18 @@ def test_nonuniformimage_setnorm():
     im.set_norm(plt.Normalize())
 
 
+@needs_pillow
+def test_jpeg_2d():
+    # smoke test that mode-L pillow images work.
+    imd = np.ones((10, 10), dtype='uint8')
+    for i in range(10):
+        imd[i, :] = np.linspace(0.0, 1.0, 10) * 255
+    im = Image.new('L', (10, 10))
+    im.putdata(imd.flatten())
+    fig, ax = plt.subplots()
+    ax.imshow(im)
+
+
 @needs_pillow
 def test_jpeg_alpha():
     plt.figure(figsize=(1, 1), dpi=300)
@@ -855,7 +867,18 @@ def test_imshow_bignumbers():
     img = np.array([[1, 2, 1e12],[3, 1, 4]], dtype=np.uint64)
     pc = ax.imshow(img)
     pc.set_clim(0, 5)
-    plt.show()
+
+
+@image_comparison(baseline_images=['imshow_bignumbers_real'],
+                  remove_text=True, style='mpl20',
+                  extensions=['png'])
+def test_imshow_bignumbers_real():
+    # putting a big number in an array of integers shouldn't
+    # ruin the dynamic range of the resolved bits.
+    fig, ax = plt.subplots()
+    img = np.array([[2., 1., 1.e22],[4., 1., 3.]])
+    pc = ax.imshow(img)
+    pc.set_clim(0, 5)
 
 
 @pytest.mark.parametrize(