diff --git a/doc/api/next_api_changes/2018-11-23-AL.rst b/doc/api/next_api_changes/2018-11-23-AL.rst
new file mode 100644
index 000000000000..1936d3a8d97c
--- /dev/null
+++ b/doc/api/next_api_changes/2018-11-23-AL.rst
@@ -0,0 +1,6 @@
+Log-scaled axes avoid having zero or only one tick
+``````````````````````````````````````````````````
+
+When the default `LogLocator` would generate no ticks for an axis (e.g., an
+axis with limits from 0.31 to 0.39) or only a single tick, it now instead falls
+back on the linear `AutoLocator` to pick reasonable tick positions.
diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
index 69fa646f6b85..5a7b8f446349 100644
--- a/lib/matplotlib/tests/test_ticker.py
+++ b/lib/matplotlib/tests/test_ticker.py
@@ -1,7 +1,7 @@
 import warnings
 
 import numpy as np
-from numpy.testing import assert_almost_equal
+from numpy.testing import assert_almost_equal, assert_array_equal
 import pytest
 
 import matplotlib
@@ -179,6 +179,11 @@ def test_basic(self):
         test_value = np.array([0.5, 1., 2., 4., 8., 16., 32., 64., 128., 256.])
         assert_almost_equal(loc.tick_values(1, 100), test_value)
 
+    def test_switch_to_autolocator(self):
+        loc = mticker.LogLocator(subs="all")
+        assert_array_equal(loc.tick_values(0.45, 0.55),
+                           [0.44, 0.46, 0.48, 0.5, 0.52, 0.54, 0.56])
+
     def test_set_params(self):
         """
         Create log locator with default value, base=10.0, subs=[1.0],
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index fb39bfba9dc7..3e299b31303b 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -2165,13 +2165,13 @@ def tick_values(self, vmin, vmax):
                     "log-scaled.")
 
         _log.debug('vmin %s vmax %s', vmin, vmax)
-        vmin = math.log(vmin) / math.log(b)
-        vmax = math.log(vmax) / math.log(b)
 
         if vmax < vmin:
             vmin, vmax = vmax, vmin
+        log_vmin = math.log(vmin) / math.log(b)
+        log_vmax = math.log(vmax) / math.log(b)
 
-        numdec = math.floor(vmax) - math.ceil(vmin)
+        numdec = math.floor(log_vmax) - math.ceil(log_vmin)
 
         if isinstance(self._subs, str):
             _first = 2.0 if self._subs == 'auto' else 1.0
@@ -2195,11 +2195,12 @@ def tick_values(self, vmin, vmax):
             while numdec // stride + 1 > numticks:
                 stride += 1
 
-        # Does subs include anything other than 1?
+        # Does subs include anything other than 1?  Essentially a hack to know
+        # whether we're a major or a minor locator.
         have_subs = len(subs) > 1 or (len(subs) == 1 and subs[0] != 1.0)
 
-        decades = np.arange(math.floor(vmin) - stride,
-                            math.ceil(vmax) + 2 * stride, stride)
+        decades = np.arange(math.floor(log_vmin) - stride,
+                            math.ceil(log_vmax) + 2 * stride, stride)
 
         if hasattr(self, '_transform'):
             ticklocs = self._transform.inverted().transform(decades)
@@ -2207,20 +2208,27 @@ def tick_values(self, vmin, vmax):
                 if stride == 1:
                     ticklocs = np.ravel(np.outer(subs, ticklocs))
                 else:
-                    # no ticklocs if we have more than one decade
-                    # between major ticks.
-                    ticklocs = []
+                    # No ticklocs if we have >1 decade between major ticks.
+                    ticklocs = np.array([])
         else:
             if have_subs:
-                ticklocs = []
                 if stride == 1:
-                    for decadeStart in b ** decades:
-                        ticklocs.extend(subs * decadeStart)
+                    ticklocs = np.concatenate(
+                        [subs * decade_start for decade_start in b ** decades])
+                else:
+                    ticklocs = np.array([])
             else:
                 ticklocs = b ** decades
 
         _log.debug('ticklocs %r', ticklocs)
-        return self.raise_if_exceeds(np.asarray(ticklocs))
+        if (len(subs) > 1
+                and stride == 1
+                and ((vmin <= ticklocs) & (ticklocs <= vmax)).sum() <= 1):
+            # If we're a minor locator *that expects at least two ticks per
+            # decade* and the major locator stride is 1 and there's no more
+            # than one minor tick, switch to AutoLocator.
+            return AutoLocator().tick_values(vmin, vmax)
+        return self.raise_if_exceeds(ticklocs)
 
     def view_limits(self, vmin, vmax):
         'Try to choose the view limits intelligently'