diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 045e68925766..3c383ef71970 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2632,7 +2632,6 @@ def _update_title_position(self, renderer):
         Update the title position based on the bounding box enclosing
         all the ticklabels and x-axis spine and xlabel...
         """
-
         if self._autotitlepos is not None and not self._autotitlepos:
             _log.debug('title position was updated manually, not adjusting')
             return
@@ -2655,7 +2654,7 @@ def _update_title_position(self, renderer):
                     else:
                         ax.apply_aspect()
                     axs = axs + [ax]
-            top = 0
+            top = -np.Inf
             for ax in axs:
                 if (ax.xaxis.get_ticks_position() in ['top', 'unknown']
                         or ax.xaxis.get_label_position() == 'top'):
@@ -2664,6 +2663,11 @@ def _update_title_position(self, renderer):
                     bb = ax.get_window_extent(renderer)
                 if bb is not None:
                     top = max(top, bb.ymax)
+            if top < 0:
+                # the top of axes is not even on the figure, so don't try and
+                # automatically place it.
+                _log.debug('top of axes not in the figure, so title not moved')
+                return
             if title.get_window_extent(renderer).ymin < top:
                 _, y = self.transAxes.inverted().transform((0, top))
                 title.set_position((x, y))
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 84b13405af33..664a478bfe63 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -5533,6 +5533,19 @@ def test_title_xticks_top_both():
     assert ax.title.get_position()[1] > 1.04
 
 
+def test_title_no_move_off_page():
+    # If an axes is off the figure (ie. if it is cropped during a save)
+    # make sure that the automatic title repositioning does not get done.
+    mpl.rcParams['axes.titley'] = None
+    fig = plt.figure()
+    ax = fig.add_axes([0.1, -0.5, 0.8, 0.2])
+    ax.tick_params(axis="x",
+                   bottom=True, top=True, labelbottom=True, labeltop=True)
+    tt = ax.set_title('Boo')
+    fig.canvas.draw()
+    assert tt.get_position()[1] == 1.0
+
+
 def test_offset_label_color():
     # Tests issue 6440
     fig = plt.figure()
diff --git a/lib/matplotlib/tests/test_pickle.py b/lib/matplotlib/tests/test_pickle.py
index 4ab73e402076..c302bbbab98a 100644
--- a/lib/matplotlib/tests/test_pickle.py
+++ b/lib/matplotlib/tests/test_pickle.py
@@ -1,6 +1,5 @@
 from io import BytesIO
 import pickle
-import platform
 
 import numpy as np
 import pytest