diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
index b0ecb72dfdb4..02c2ecfaeff0 100644
--- a/lib/matplotlib/tests/test_ticker.py
+++ b/lib/matplotlib/tests/test_ticker.py
@@ -183,6 +183,10 @@ 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])
+        # check that we *skip* 1.0, and 10, because this is a minor locator
+        loc = mticker.LogLocator(subs=np.arange(2, 10))
+        assert 1.0 not in loc.tick_values(0.9, 20.)
+        assert 10.0 not in loc.tick_values(0.9, 20.)
 
     def test_set_params(self):
         """
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index 89e077a04262..c68ef258dcd9 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -2093,9 +2093,7 @@ def is_decade(x, base=10):
 
 
 def is_close_to_int(x):
-    if not np.isfinite(x):
-        return False
-    return abs(x - round(x)) < 1e-10
+    return abs(x - np.round(x)) < 1e-10
 
 
 class LogLocator(Locator):
@@ -2256,7 +2254,12 @@ def tick_values(self, vmin, vmax):
             # 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)
+            ticklocs = AutoLocator().tick_values(vmin, vmax)
+            # Don't overstrike the major labels.  Assumes major locs are
+            # at b = self._base
+            ticklocs = ticklocs[
+                ~is_close_to_int(np.log(ticklocs) / np.log(b))]
+            return ticklocs
         return self.raise_if_exceeds(ticklocs)
 
     def view_limits(self, vmin, vmax):