diff --git a/lib/matplotlib/__init__.py b/lib/matplotlib/__init__.py
index c5accc3c3..472680fe6 100644
--- a/lib/matplotlib/__init__.py
+++ b/lib/matplotlib/__init__.py
@@ -130,7 +130,6 @@ from matplotlib.compat import subprocess
 from matplotlib.rcsetup import defaultParams, validate_backend, cycler
 
 import numpy
-from six.moves.urllib.request import urlopen
 from six.moves import reload_module as reload
 
 # Get the version from the _version.py versioneer file. For a git checkout,
@@ -1023,6 +1022,7 @@ def _url_lines(f):
 @contextlib.contextmanager
 def _open_file_or_url(fname):
     if is_url(fname):
+        from six.moves.urllib.request import urlopen
         f = urlopen(fname)
         yield _url_lines(f)
         f.close()
diff --git a/lib/matplotlib/_layoutbox.py b/lib/matplotlib/_layoutbox.py
index cb6f03158..0cc6bdf88 100644
--- a/lib/matplotlib/_layoutbox.py
+++ b/lib/matplotlib/_layoutbox.py
@@ -20,7 +20,6 @@ from __future__ import (absolute_import, division, print_function,
                         unicode_literals)
 
 import itertools
-import kiwisolver as kiwi
 import logging
 import numpy as np
 import warnings
@@ -58,6 +57,8 @@ class LayoutBox(object):
                  tightheight=False, artist=None,
                  lower_left=(0, 0), upper_right=(1, 1), pos=False,
                  subplot=False, h_pad=None, w_pad=None):
+        import kiwisolver as kiwi
+
         Variable = kiwi.Variable
         self.parent = parent
         self.name = name
diff --git a/lib/matplotlib/backends/backend_agg.py b/lib/matplotlib/backends/backend_agg.py
index aff6cddf4..c4d2d0713 100644
--- a/lib/matplotlib/backends/backend_agg.py
+++ b/lib/matplotlib/backends/backend_agg.py
@@ -46,7 +46,6 @@ from matplotlib.transforms import Bbox, BboxBase
 from matplotlib import colors as mcolors
 
 from matplotlib.backends._backend_agg import RendererAgg as _RendererAgg
-from matplotlib import _png
 
 try:
     from PIL import Image
@@ -514,6 +513,8 @@ class FigureCanvasAgg(FigureCanvasBase):
     print_rgba = print_raw
 
     def print_png(self, filename_or_obj, *args, **kwargs):
+        from matplotlib import _png
+
         FigureCanvasAgg.draw(self)
         renderer = self.get_renderer()
         original_dpi = renderer.dpi
diff --git a/lib/matplotlib/cbook/__init__.py b/lib/matplotlib/cbook/__init__.py
index dcb2d0549..3dfc49589 100644
--- a/lib/matplotlib/cbook/__init__.py
+++ b/lib/matplotlib/cbook/__init__.py
@@ -16,7 +16,6 @@ import datetime
 import errno
 import functools
 import glob
-import gzip
 import io
 from itertools import repeat
 import locale
@@ -597,6 +596,7 @@ def to_filehandle(fname, flag='rU', return_opened=False, encoding=None):
             flag=flag, return_opened=return_opened, encoding=encoding)
     if isinstance(fname, six.string_types):
         if fname.endswith('.gz'):
+            import gzip
             # get rid of 'U' in flag for gzipped files.
             flag = flag.replace('U', '')
             fh = gzip.open(fname, flag)
diff --git a/lib/matplotlib/contour.py b/lib/matplotlib/contour.py
index f6fdfd61c..c06431910 100644
--- a/lib/matplotlib/contour.py
+++ b/lib/matplotlib/contour.py
@@ -11,7 +11,6 @@ import warnings
 import matplotlib as mpl
 import numpy as np
 from numpy import ma
-import matplotlib._contour as _contour
 import matplotlib.path as mpath
 import matplotlib.ticker as ticker
 import matplotlib.cm as cm
@@ -1469,6 +1468,8 @@ class QuadContourSet(ContourSet):
             self._mins = args[0]._mins
             self._maxs = args[0]._maxs
         else:
+            import matplotlib._contour as contour
+
             self._corner_mask = kwargs.pop('corner_mask', None)
             if self._corner_mask is None:
                 self._corner_mask = mpl.rcParams['contour.corner_mask']
diff --git a/lib/matplotlib/font_manager.py b/lib/matplotlib/font_manager.py
index 5900fc9b1..f23f5a438 100644
--- a/lib/matplotlib/font_manager.py
+++ b/lib/matplotlib/font_manager.py
@@ -55,7 +55,7 @@ except ImportError:
 import warnings
 import logging
 
-from matplotlib import afm, cbook, ft2font, rcParams, get_cachedir
+from matplotlib import cbook, ft2font, rcParams, get_cachedir
 from matplotlib.compat import subprocess
 from matplotlib.fontconfig_pattern import (
     parse_fontconfig_pattern, generate_fontconfig_pattern)
@@ -569,6 +569,7 @@ def createFontList(fontfiles, fontext='ttf'):
         else:
             seen.add(fname)
         if fontext == 'afm':
+            from matplotlib import afm
             try:
                 fh = open(fpath, 'rb')
             except EnvironmentError:
diff --git a/lib/matplotlib/image.py b/lib/matplotlib/image.py
index 3ea0cb70d..5b3056a18 100644
--- a/lib/matplotlib/image.py
+++ b/lib/matplotlib/image.py
@@ -26,7 +26,6 @@ import matplotlib.cbook as cbook
 
 # For clarity, names from _image are given explicitly in this module:
 import matplotlib._image as _image
-import matplotlib._png as _png
 
 # For user convenience, the names from _image are also imported into
 # the image namespace:
@@ -623,6 +622,7 @@ class _ImageBase(martist.Artist, cm.ScalarMappable):
 
     def write_png(self, fname):
         """Write the image to png file with fname"""
+        from matplotlib import _png
         im = self.to_rgba(self._A[::-1] if self.origin == 'lower' else self._A,
                           bytes=True, norm=True)
         _png.write_png(im, fname)
@@ -1335,7 +1335,11 @@ def imread(fname, format=None):
         with Image.open(fname) as image:
             return pil_to_array(image)
 
-    handlers = {'png': _png.read_png, }
+    def read_png(*args, **kwargs):
+        from matplotlib import _png
+        return _png.read_png(*args, **kwargs)
+
+    handlers = {'png': read_png, }
     if format is None:
         if isinstance(fname, six.string_types):
             parsed = urlparse(fname)
diff --git a/lib/matplotlib/mathtext.py b/lib/matplotlib/mathtext.py
index dee778b0d..428582ace 100644
--- a/lib/matplotlib/mathtext.py
+++ b/lib/matplotlib/mathtext.py
@@ -35,7 +35,7 @@ from pyparsing import (
 
 ParserElement.enablePackrat()
 
-from matplotlib import _png, colors as mcolors, get_data_path, rcParams
+from matplotlib import colors as mcolors, get_data_path, rcParams
 from matplotlib.afm import AFM
 from matplotlib.cbook import Bunch, get_realpath_and_stat, maxdict
 from matplotlib.ft2font import FT2Image, KERNING_DEFAULT, LOAD_NO_HINTING
@@ -3379,6 +3379,7 @@ class MathTextParser(object):
         Returns the offset of the baseline from the bottom of the
         image in pixels.
         """
+        from matplotlib import _png
         rgba, depth = self.to_rgba(texstr, color=color, dpi=dpi, fontsize=fontsize)
         _png.write_png(rgba, filename)
         return depth
diff --git a/lib/matplotlib/tri/triangulation.py b/lib/matplotlib/tri/triangulation.py
index b80aaf87b..45bf9eb5c 100644
--- a/lib/matplotlib/tri/triangulation.py
+++ b/lib/matplotlib/tri/triangulation.py
@@ -3,8 +3,6 @@ from __future__ import (absolute_import, division, print_function,
 
 import six
 
-import matplotlib._tri as _tri
-import matplotlib._qhull as _qhull
 import numpy as np
 
 
@@ -39,6 +37,8 @@ class Triangulation(object):
     triangles formed from colinear points, or overlapping triangles.
     """
     def __init__(self, x, y, triangles=None, mask=None):
+        from matplotlib import _qhull
+
         self.x = np.asarray(x, dtype=np.float64)
         self.y = np.asarray(y, dtype=np.float64)
         if self.x.shape != self.y.shape or self.x.ndim != 1:
@@ -103,6 +103,7 @@ class Triangulation(object):
     def get_cpp_triangulation(self):
         # Return the underlying C++ Triangulation object, creating it
         # if necessary.
+        from matplotlib import _tri
         if self._cpp_triangulation is None:
             self._cpp_triangulation = _tri.Triangulation(
                 self.x, self.y, self.triangles, self.mask, self._edges,