diff --git a/doc/users/whats_new/offset-text-choice.rst b/doc/users/whats_new/offset-text-choice.rst
new file mode 100644
index 000000000000..4ffdc890c5be
--- /dev/null
+++ b/doc/users/whats_new/offset-text-choice.rst
@@ -0,0 +1,6 @@
+Improved offset text choice
+---------------------------
+The default offset-text choice was changed to only use significant digits that
+are common to all ticks (e.g. 1231..1239 -> 1230, instead of 1231), except when
+they straddle a relatively large multiple of a power of ten, in which case that
+multiple is chosen (e.g. 1999..2001->2000).
diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
index 438be20aa7ce..00f7f5fe8e27 100644
--- a/lib/matplotlib/tests/test_ticker.py
+++ b/lib/matplotlib/tests/test_ticker.py
@@ -3,7 +3,7 @@
 
 from matplotlib.externals import six
 import nose.tools
-from nose.tools import assert_raises
+from nose.tools import assert_equal, assert_raises
 from numpy.testing import assert_almost_equal
 import numpy as np
 import matplotlib
@@ -159,6 +159,53 @@ def test_SymmetricalLogLocator_set_params():
     nose.tools.assert_equal(sym.numticks, 8)
 
 
+@cleanup
+def test_ScalarFormatter_offset_value():
+    fig, ax = plt.subplots()
+    formatter = ax.get_xaxis().get_major_formatter()
+
+    def check_offset_for(left, right, offset):
+        ax.set_xlim(left, right)
+        # Update ticks.
+        next(ax.get_xaxis().iter_ticks())
+        assert_equal(formatter.offset, offset)
+
+    test_data = [(123, 189, 0),
+                 (-189, -123, 0),
+                 (12341, 12349, 12340),
+                 (-12349, -12341, -12340),
+                 (99999.5, 100010.5, 100000),
+                 (-100010.5, -99999.5, -100000),
+                 (99990.5, 100000.5, 100000),
+                 (-100000.5, -99990.5, -100000),
+                 (1233999, 1234001, 1234000),
+                 (-1234001, -1233999, -1234000),
+                 (1, 1, 1),
+                 (123, 123, 120),
+                 # Test cases courtesy of @WeatherGod
+                 (.4538, .4578, .45),
+                 (3789.12, 3783.1, 3780),
+                 (45124.3, 45831.75, 45000),
+                 (0.000721, 0.0007243, 0.00072),
+                 (12592.82, 12591.43, 12590),
+                 (9., 12., 0),
+                 (900., 1200., 0),
+                 (1900., 1200., 0),
+                 (0.99, 1.01, 1),
+                 (9.99, 10.01, 10),
+                 (99.99, 100.01, 100),
+                 (5.99, 6.01, 6),
+                 (15.99, 16.01, 16),
+                 (-0.452, 0.492, 0),
+                 (-0.492, 0.492, 0),
+                 (12331.4, 12350.5, 12300),
+                 (-12335.3, 12335.3, 0)]
+
+    for left, right, offset in test_data:
+        yield check_offset_for, left, right, offset
+        yield check_offset_for, right, left, offset
+
+
 def _logfe_helper(formatter, base, locs, i, expected_result):
     vals = base**locs
     labels = [formatter(x, pos) for (x, pos) in zip(vals, i)]
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index 872997dc8afb..b22ee19ae68c 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -159,6 +159,7 @@
 from matplotlib.externals import six
 
 import decimal
+import itertools
 import locale
 import math
 import numpy as np
@@ -635,33 +636,50 @@ def set_locs(self, locs):
             vmin, vmax = self.axis.get_view_interval()
             d = abs(vmax - vmin)
             if self._useOffset:
-                self._set_offset(d)
+                self._compute_offset()
             self._set_orderOfMagnitude(d)
             self._set_format(vmin, vmax)
 
-    def _set_offset(self, range):
-        # offset of 20,001 is 20,000, for example
+    def _compute_offset(self):
         locs = self.locs
-
-        if locs is None or not len(locs) or range == 0:
+        if locs is None or not len(locs):
             self.offset = 0
             return
+        # Restrict to visible ticks.
         vmin, vmax = sorted(self.axis.get_view_interval())
         locs = np.asarray(locs)
         locs = locs[(vmin <= locs) & (locs <= vmax)]
-        ave_loc = np.mean(locs)
-        if len(locs) and ave_loc:  # dont want to take log10(0)
-            ave_oom = math.floor(math.log10(np.mean(np.absolute(locs))))
-            range_oom = math.floor(math.log10(range))
-
-            if np.absolute(ave_oom - range_oom) >= 3:  # four sig-figs
-                p10 = 10 ** range_oom
-                if ave_loc < 0:
-                    self.offset = (math.ceil(np.max(locs) / p10) * p10)
-                else:
-                    self.offset = (math.floor(np.min(locs) / p10) * p10)
-            else:
-                self.offset = 0
+        if not len(locs):
+            self.offset = 0
+            return
+        lmin, lmax = locs.min(), locs.max()
+        # Only use offset if there are at least two ticks and every tick has
+        # the same sign.
+        if lmin == lmax or lmin <= 0 <= lmax:
+            self.offset = 0
+            return
+        # min, max comparing absolute values (we want division to round towards
+        # zero so we work on absolute values).
+        abs_min, abs_max = sorted([abs(float(lmin)), abs(float(lmax))])
+        sign = math.copysign(1, lmin)
+        # What is the smallest power of ten such that abs_min and abs_max are
+        # equal up to that precision?
+        # Note: Internally using oom instead of 10 ** oom avoids some numerical
+        # accuracy issues.
+        oom_max = math.ceil(math.log10(abs_max))
+        oom = 1 + next(oom for oom in itertools.count(oom_max, -1)
+                       if abs_min // 10 ** oom != abs_max // 10 ** oom)
+        if (abs_max - abs_min) / 10 ** oom <= 1e-2:
+            # Handle the case of straddling a multiple of a large power of ten
+            # (relative to the span).
+            # What is the smallest power of ten such that abs_min and abs_max
+            # are no more than 1 apart at that precision?
+            oom = 1 + next(oom for oom in itertools.count(oom_max, -1)
+                           if abs_max // 10 ** oom - abs_min // 10 ** oom > 1)
+        # Only use offset if it saves at least two significant digits.
+        self.offset = (sign * (abs_max // 10 ** oom) * 10 ** oom
+                       if abs_max // 10 ** oom >= 10
+                       else 0)
 
     def _set_orderOfMagnitude(self, range):
         # if scientific notation is to be used, find the appropriate exponent