diff --git a/doc/users/whats_new/adjustable_xlim_ylim.rst b/doc/users/whats_new/adjustable_xlim_ylim.rst
@@ -0,0 +1,13 @@
+New ``'xlim'`` and ``'ylim'`` options for ``adjustable`` argument
+-----------------------------------------------------------------
+
+The ``adjustable`` argument to the :meth:`~matplotlib.axes.Axes.set_aspect`
+method (and the same argument which can be specified when initializing
+:meth:`~matplotlib.axes.Axes`) can take two new values: ``'xlim'`` and
+``'ylim'``. Previously, users could pass the ``'datalim'`` value to indicate
+that Matplotlib should adjust the limits as needed so as to be able to avoid
+modifying the position and aspect ratio of the axes, but it was impossible to
+know deterministically whether Matplotlib would modify the x or y limits. The
+new ``'xlim'`` and ``'ylim'`` options behave like ``'datalim'`` except that
+``'xlim'`` causes only the x limits to be adjusted, and ``'ylim'`` causes only
+the y limits to be adjusted.
diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
@@ -438,7 +438,8 @@ def __init__(self, fig, rect,
           ================   =========================================
           Keyword            Description
           ================   =========================================
-          *adjustable*       [ 'box' | 'datalim' | 'box-forced']
+          *adjustable*       [ 'box' | 'datalim' | 'xlim' | 'ylim' | \
+                               'box-forced' ]
           *alpha*            float: the alpha transparency (can be None)
           *anchor*           [ 'C', 'SW', 'S', 'SE', 'E', 'NE', 'N',
                                'NW', 'W' ]
@@ -1271,6 +1272,8 @@ def set_aspect(self, aspect, adjustable=None, anchor=None):
           ============   =====================================
           'box'          change physical size of axes
           'datalim'      change xlim or ylim
+          'xlim'         change xlim
+          'ylim'         change ylim
           'box-forced'   same as 'box', but axes can be shared
           ============   =====================================
 
@@ -1307,9 +1310,9 @@ def get_adjustable(self):
 
     def set_adjustable(self, adjustable):
         """
-        ACCEPTS: [ 'box' | 'datalim' | 'box-forced']
+        ACCEPTS: [ 'box' | 'datalim' | 'xlim' | 'ylim' | 'box-forced']
         """
-        if adjustable in ('box', 'datalim', 'box-forced'):
+        if adjustable in ('box', 'datalim', 'xlim', 'ylim', 'box-forced'):
             if self in self._shared_x_axes or self in self._shared_y_axes:
                 if adjustable == 'box':
                     raise ValueError(
@@ -1482,11 +1485,27 @@ def apply_aspect(self, position=None):
                    self not in self._shared_x_axes)
         changey = (self in self._shared_x_axes and
                    self not in self._shared_y_axes)
+
         if changex and changey:
-            warnings.warn("adjustable='datalim' cannot work with shared "
-                          "x and y axes")
+            warnings.warn("adjustable='{0}' cannot work with shared "
+                          "x and y axes".format(self._adjustable))
+            return
+
+        if self._adjustable == 'xlim' and changey:
+            warnings.warn("adjustable='xlim' cannot work with shared "
+                          "x axes".format(self._adjustable))
+            return
+
+        if self._adjustable == 'ylim' and changex:
+            warnings.warn("adjustable='ylim' cannot work with shared "
+                          "y axes".format(self._adjustable))
             return
-        if changex:
+
+        if self._adjustable == 'xlim':
+            adjust_y = False
+        elif self._adjustable == 'ylim':
+            adjust_y = True
+        elif changex:
             adjust_y = False
         else:
             if xmarg > xm and ymarg > ym:
@@ -1495,6 +1514,7 @@ def apply_aspect(self, position=None):
             else:
                 adjy = y_expander > 0
             adjust_y = changey or adjy  # (Ymarg > xmarg)
+
         if adjust_y:
             yc = 0.5 * (ymin + ymax)
             y0 = yc - Ysize / 2.0

diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
@@ -5149,3 +5149,95 @@ def test_twinx_knows_limits():
     ax2.plot([0, 0.5], [1, 2])
 
     assert((xtwin.viewLim.intervalx == ax2.viewLim.intervalx).all())
+
+
+def test_adjustable_limits():
+
+    # Test the 'datalim', 'xlim', and 'ylim' options
+
+    image = np.ones((5, 5))
+
+    # First, we test adjustable='datalim'. Here, whether xlim or ylim are
+    # changed is up to Matplotlib.
+
+    fig = plt.figure(figsize=(6, 4))
+    ax = fig.add_axes([0, 0, 1, 1], aspect='equal')
+    ax.imshow(image, origin='lower')
+
+    # Since the axes has a landscape aspect ratio, the image should fit
+    # vertically and have white padding horizontally:
+    ax.set_adjustable('datalim')
+    ax.apply_aspect()
+    assert_allclose(ax.get_xlim(), [-1.75, 5.75])
+    assert_allclose(ax.get_ylim(), [-0.5, 4.5])
+
+    # Because of the way Matplotlib computes the aspect internally, it turns
+    # out that in this scenario ylim is the adjustable, so even if we change
+    # ylim, xlim will stay the same and ylim will get adjusted. This could be
+    # improved in future by checking in set_xlim and set_ylim whether
+    # adjustable='datalim' and try and make sure this value is respected.
+    ax.set_ylim(4, 5)
+    ax.apply_aspect()
+    assert_allclose(ax.get_xlim(), [-1.75, 5.75])
+    assert_allclose(ax.get_ylim(), [2, 7])
+
+    # Similarly, if xlim is changed, the values are not necessarily respected
+    # and in fact ylim is the one that stays constant. This behavior is the
+    # reason for adding explicit adjustable='xlim' and adjustable='ylim'
+    # options.
+    ax.set_xlim(1, 4)
+    ax.apply_aspect()
+    assert_allclose(ax.get_xlim(), [-1.25, 6.25])
+    assert_allclose(ax.get_ylim(), [2, 7])
+
+    # We now test adjustable='xlim', which should behave in a much more
+    # predictable way.
+
+    fig = plt.figure(figsize=(6, 4))
+    ax = fig.add_axes([0, 0, 1, 1], aspect='equal')
+    ax.imshow(image, origin='lower')
+
+    ax.set_adjustable('xlim')
+    ax.apply_aspect()
+    assert_allclose(ax.get_xlim(), [-1.75, 5.75])
+    assert_allclose(ax.get_ylim(), [-0.5, 4.5])
+
+    # Changing ylim results in ylim changing predictably and xlim getting
+    # adjusted
+    ax.set_ylim(4, 6)
+    ax.apply_aspect()
+    assert_allclose(ax.get_xlim(), [0.5, 3.5])
+    assert_allclose(ax.get_ylim(), [4, 6])
+
+    # Changing xlim results in xlim adjusting itself and ylim staying the same
+    ax.set_xlim(2, 4)
+    ax.apply_aspect()
+    assert_allclose(ax.get_xlim(), [1.5, 4.5])
+    assert_allclose(ax.get_ylim(), [4, 6])
+
+    # Finally we test adjustable='ylim', which should behave similarly to
+    # 'xlim'
+
+    fig = plt.figure(figsize=(6, 4))
+    ax = fig.add_axes([0, 0, 1, 1], aspect='equal')
+    ax.imshow(image, origin='lower')
+
+    # In the case where ylim is the adjustable, the image will fill the axes
+    # horizontally.
+    ax.set_adjustable('ylim')
+    ax.apply_aspect()
+    assert_allclose(ax.get_xlim(), [-0.5, 4.5])
+    assert_allclose(ax.get_ylim(), [1 / 3., 11 / 3.])
+
+    # Changing xlim results in xlim changing predictably and ylim getting
+    # adjusted
+    ax.set_xlim(4, 6)
+    ax.apply_aspect()
+    assert_allclose(ax.get_xlim(), [4, 6])
+    assert_allclose(ax.get_ylim(), [4 / 3., 8 / 3.])
+
+    # Changing ylim results in ylim adjusting itself and xlim staying the same
+    ax.set_ylim(2, 4)
+    ax.apply_aspect()
+    assert_allclose(ax.get_xlim(), [4, 6])
+    assert_allclose(ax.get_ylim(), [7 / 3., 11 / 3.])