diff --git a/lib/matplotlib/colorbar.py b/lib/matplotlib/colorbar.py
index a48cb9bedbf6..13c12a5f90c1 100644
--- a/lib/matplotlib/colorbar.py
+++ b/lib/matplotlib/colorbar.py
@@ -551,8 +551,8 @@ def add_lines(self, levels, colors, linewidths, erase=True):
 
     def _ticker(self):
         '''
-        Return two sequences: ticks (colorbar data locations)
-        and ticklabels (strings).
+        Return the sequence of ticks (colorbar data locations),
+        ticklabels (strings), and the corresponding offset string.
         '''
         locator = self.locator
         formatter = self.formatter
@@ -653,6 +653,9 @@ def _process_values(self, b=None):
             self._values = v
             return
         else:
+            self.norm.vmin, self.norm.vmax = mtrans.nonsingular(self.norm.vmin,
+                                                                self.norm.vmax,
+                                                                expander=0.1)
             if not self.norm.scaled():
                 self.norm.vmin = 0
                 self.norm.vmax = 1
@@ -817,24 +820,21 @@ def _locate(self, x):
             # as to make the interpolation more accurate.
             b = self.norm(self._boundaries, clip=False).filled()
             xn = self.norm(x, clip=False).filled()
+
         # The rest is linear interpolation with extrapolation at ends.
-        y = self._y
-        N = len(b)
         ii = np.searchsorted(b, xn)
         i0 = ii - 1
-        itop = (ii == N)
+        itop = (ii == len(b))
         ibot = (ii == 0)
         i0[itop] -= 1
         ii[itop] -= 1
         i0[ibot] += 1
         ii[ibot] += 1
 
-        #db = b[ii] - b[i0]
         db = np.take(b, ii) - np.take(b, i0)
-        #dy = y[ii] - y[i0]
+        y = self._y
         dy = np.take(y, ii) - np.take(y, i0)
         z = np.take(y, i0) + (xn - np.take(b, i0)) * dy / db
-
         return z
 
     def set_alpha(self, alpha):
diff --git a/lib/matplotlib/tests/baseline_images/test_colorbar/colorbar_single_scatter.png b/lib/matplotlib/tests/baseline_images/test_colorbar/colorbar_single_scatter.png
new file mode 100644
index 000000000000..fd6f35d1b9c5
Binary files /dev/null and b/lib/matplotlib/tests/baseline_images/test_colorbar/colorbar_single_scatter.png differ
diff --git a/lib/matplotlib/tests/test_colorbar.py b/lib/matplotlib/tests/test_colorbar.py
index 4dd2e915a2a6..4b6e05d6a0d2 100644
--- a/lib/matplotlib/tests/test_colorbar.py
+++ b/lib/matplotlib/tests/test_colorbar.py
@@ -195,6 +195,22 @@ def test_gridspec_make_colorbar():
     plt.subplots_adjust(top=0.95, right=0.95, bottom=0.2, hspace=0.25)
 
 
+@image_comparison(baseline_images=['colorbar_single_scatter'],
+                  extensions=['png'], remove_text=True,
+                  savefig_kwarg={'dpi': 40})
+def test_colorbar_single_scatter():
+    # Issue #2642: if a path collection has only one entry,
+    # the norm scaling within the colorbar must ensure a
+    # finite range, otherwise a zero denominator will occur in _locate.
+    plt.figure()
+    x = np.arange(4)
+    y = x.copy()
+    z = np.ma.masked_greater(np.arange(50, 54), 50)
+    cmap = plt.get_cmap('jet', 16)
+    cs = plt.scatter(x, y, z, c=z, cmap=cmap)
+    plt.colorbar(cs)
+
+
 if __name__ == '__main__':
     import nose
     nose.runmodule(argv=['-s', '--with-doctest'], exit=False)