diff --git a/examples/pylab_examples/log_demo.py b/examples/pylab_examples/log_demo.py
index bf7372191fc1..eeb30f36583b 100644
--- a/examples/pylab_examples/log_demo.py
+++ b/examples/pylab_examples/log_demo.py
@@ -21,7 +21,7 @@
 plt.subplot(223)
 plt.loglog(t, 20*np.exp(-t/10.0), basex=2)
 plt.grid(True)
-plt.title('loglog base 4 on x')
+plt.title('loglog base 2 on x')
 
 # with errorbars: clip non-positive values
 ax = plt.subplot(224)
diff --git a/lib/matplotlib/scale.py b/lib/matplotlib/scale.py
index 8784ca495905..32359b46a9c5 100644
--- a/lib/matplotlib/scale.py
+++ b/lib/matplotlib/scale.py
@@ -306,7 +306,7 @@ def set_default_locators_and_formatters(self, axis):
         axis.set_major_locator(LogLocator(self.base))
         axis.set_major_formatter(LogFormatterSciNotation(self.base))
         axis.set_minor_locator(LogLocator(self.base, self.subs))
-        axis.set_minor_formatter(NullFormatter())
+        axis.set_minor_formatter(LogFormatterSciNotation(self.base, self.subs))
 
     def get_transform(self):
         """
diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
index 069c7c194a8d..531367658326 100644
--- a/lib/matplotlib/tests/test_ticker.py
+++ b/lib/matplotlib/tests/test_ticker.py
@@ -250,13 +250,16 @@ def test_LogFormatter_sublabel():
     assert np.all(show_major_labels)
     _sub_labels(ax.xaxis, subs=[])
 
-    # axis range at 2 to 3 decades, label sub 3
+    # For the next two, if the numdec threshold in LogFormatter.set_locs
+    # were 3, then the label sub would be 3 for 2-3 decades and (2,5)
+    # for 1-2 decades.  With a threshold of 1, subs are not labeled.
+    # axis range at 2 to 3 decades
     ax.set_xlim(1, 800)
-    _sub_labels(ax.xaxis, subs=[3])
+    _sub_labels(ax.xaxis, subs=[])
 
-    # axis range at 1 to 2 decades, label subs 2 and 5
+    # axis range at 1 to 2 decades
     ax.set_xlim(1, 80)
-    _sub_labels(ax.xaxis, subs=[2, 5])
+    _sub_labels(ax.xaxis, subs=[])
 
     # axis range at 0 to 1 decades, label subs 2, 3, 6
     ax.set_xlim(1, 8)
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index f274ba71a81a..2ab5eddc87d2 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -853,7 +853,7 @@ def set_locs(self, locs):
             vmax = math.log(vmax) / math.log(b)
             numdec = abs(vmax - vmin)
 
-        if numdec > 3:
+        if numdec > 1:
             # Label only bases
             self.sublabel = set((1,))
         else:
@@ -1857,10 +1857,10 @@ def tick_values(self, vmin, vmax):
 
         numdec = math.floor(vmax) - math.ceil(vmin)
 
-        if self._subs is None:  # autosub
-            if numdec > 10:
-                subs = np.array([1.0])
-            elif numdec > 6:
+        if self._subs is None:  # autosub for minor ticks
+            if numdec > 10 or b < 3:
+                return np.array([])  # no minor ticks
+            elif numdec > 5 and b >= 6:
                 subs = np.arange(2.0, b, 2.0)
             else:
                 subs = np.arange(2.0, b)