diff --git a/doc/users/next_whats_new/2018_12_03_sphinx_plot_preserve.rst b/doc/users/next_whats_new/2018_12_03_sphinx_plot_preserve.rst
@@ -0,0 +1,61 @@
+Plot Directive `outname` and `plot_preserve_dir`
+----------------------------------------------------
+
+The Sphinx plot directive can be used to automagically generate figures for
+documentation like so:
+
+.. code-block:: rst
+
+    .. plot::
+
+       import matplotlib.pyplot as plt
+       import matplotlib.image as mpimg
+       import numpy as np
+       img = mpimg.imread('_static/stinkbug.png')
+       imgplot = plt.imshow(img)
+
+But, if you reorder the figures in the documentation then all the figures may
+need to be rebuilt. This takes time. The names given to the figures are also
+fairly meaningless, making them more difficult to index by search engines or to
+find on a filesystem.
+
+Alternatively, if you are compiling on a limited-resource service like
+ReadTheDocs, you may wish to build imagery locally to avoid hitting resource
+limits on the server. Using the new changes allows extensive dynamically
+generated imagery to be used on services like ReadTheDocs.
+
+The ``:outname:`` property
+~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+These problems are addressed through two new features in the plot directive.
+The first is the introduction of the ``:outname:`` property. It is used like
+so:
+
+.. code-block:: rst
+
+    .. plot::
+       :outname: stinkbug_plot
+
+       import matplotlib.pyplot as plt
+       import matplotlib.image as mpimg
+       import numpy as np
+       img = mpimg.imread('_static/stinkbug.png')
+       imgplot = plt.imshow(img)
+
+Without ``:outname:``, the figure generated above would normally be called,
+e.g. :file:`docfile3-4-01.png` or something equally mysterious. With
+``:outname:`` the figure generated will instead be named
+:file:`stinkbug_plot-01.png` or even :file:`stinkbug_plot.png`. This makes it
+easy to understand which output image is which and, more importantly, uniquely
+keys output images to code snippets.
+
+The ``plot_preserve_dir`` configuration value
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Setting the ``plot_preserve_dir`` configuration value to the name of a
+directory will cause all images with ``:outname:`` set to be copied to this
+directory upon generation.
+
+If an image is already in ``plot_preserve_dir`` when documentation is being
+generated, this image is copied to the build directory thereby pre-empting
+generation and reducing computation time in low-resource environments.
diff --git a/lib/matplotlib/sphinxext/plot_directive.py b/lib/matplotlib/sphinxext/plot_directive.py
@@ -70,10 +70,18 @@
         If specified, the code block will be run, but no figures will be
         inserted.  This is usually useful with the ``:context:`` option.
 
+    outname : str
+        If specified, the names of the generated plots will start with the
+        value of `:outname:`. This is handy for preserving output results if
+        code is reordered between runs. The value of `:outname:` must be
+        unique across the generated documentation.
+
 Additionally, this directive supports all of the options of the `image`
 directive, except for *target* (since plot will add its own target).  These
 include `alt`, `height`, `width`, `scale`, `align` and `class`.
 
+
+
 Configuration options
 ---------------------
 
@@ -129,12 +137,25 @@
 
     plot_template
         Provide a customized template for preparing restructured text.
+
+    plot_preserve_dir
+        Files with outnames are copied to this directory and files in this
+        directory are copied back into the build directory prior to the build
+        beginning.
+
 """
 
 import contextlib
 from io import StringIO
 import itertools
 import os
+import sys
+import shutil
+import io
+import re
+import textwrap
+import glob
+import logging
 from os.path import relpath
 from pathlib import Path
 import re
@@ -157,8 +178,14 @@
 
 __version__ = 2
 
+_log = logging.getLogger(__name__)
 
-# -----------------------------------------------------------------------------
+#Outnames must be unique. This variable stores the outnames that
+#have been seen so we can guarantee this and warn the user if a
+#duplicate is encountered.
+_outname_list = set()
+
+#------------------------------------------------------------------------------
 # Registration hook
 # -----------------------------------------------------------------------------
 
@@ -252,6 +279,7 @@ class PlotDirective(Directive):
         'context': _option_context,
         'nofigs': directives.flag,
         'encoding': directives.encoding,
+        'outname': str,
         }
 
     def run(self):
@@ -276,6 +304,7 @@ def setup(app):
     app.add_config_value('plot_apply_rcparams', False, True)
     app.add_config_value('plot_working_directory', None, True)
     app.add_config_value('plot_template', None, True)
+    app.add_config_value('plot_preserve_dir', '', True)
 
     app.connect('doctree-read', mark_plot_labels)
 
@@ -519,7 +548,7 @@ def get_plot_formats(config):
 
 def render_figures(code, code_path, output_dir, output_base, context,
                    function_name, config, context_reset=False,
-                   close_figs=False):
+                   close_figs=False, outname=''):
     """
     Run a pyplot script and save the images in *output_dir*.
 
@@ -610,7 +639,13 @@ def render_figures(code, code_path, output_dir, output_base, context,
             for fmt, dpi in formats:
                 try:
                     figman.canvas.figure.savefig(img.filename(fmt), dpi=dpi)
-                except Exception:
+                    if config.plot_preserve_dir and outname:
+                        _log.info(
+                            "Preserving '{0}' into '{1}'".format(
+                                img.filename(fmt), config.plot_preserve_dir))
+                        shutil.copy2(img.filename(fmt),
+                                     config.plot_preserve_dir)
+                except Exception as err:
                     raise PlotError(traceback.format_exc())
                 img.formats.append(fmt)
 
@@ -637,6 +672,21 @@ def run(arguments, content, options, state_machine, state, lineno):
     rst_file = document.attributes['source']
     rst_dir = os.path.dirname(rst_file)
 
+    # Get output name of the images, if the option was provided
+    outname = options.get('outname', '')
+
+    # Ensure that the outname is unique, otherwise copied images will
+    # not be what user expects
+    if outname and outname in _outname_list:
+        raise Exception("The outname '{0}' is not unique!".format(outname))
+    else:
+        _outname_list.add(outname)
+
+    if config.plot_preserve_dir:
+        # Ensure `preserve_dir` ends with a slash, otherwise `copy2`
+        # will misbehave
+        config.plot_preserve_dir = os.path.join(config.plot_preserve_dir, '')
+
     if len(arguments):
         if not config.plot_basedir:
             source_file_name = os.path.join(setup.app.builder.srcdir,
@@ -672,6 +722,11 @@ def run(arguments, content, options, state_machine, state, lineno):
     else:
         source_ext = ''
 
+    # outname, if present, overrides output_base, but preserve
+    # numbering of multi-figure code snippets
+    if outname:
+        output_base = re.sub('^[^-]*', outname, output_base)
+
     # ensure that LaTeX includegraphics doesn't choke in foo.bar.pdf filenames
     output_base = output_base.replace('.', '-')
 
@@ -718,6 +773,16 @@ def run(arguments, content, options, state_machine, state, lineno):
         build_dir_link = build_dir
     source_link = dest_dir_link + '/' + output_base + source_ext
 
+    # If we previously preserved copies of the generated figures this copies
+    # them into the build directory so that they will not be remade.
+    if config.plot_preserve_dir and outname:
+        outfiles = glob.glob(
+            os.path.join(config.plot_preserve_dir, outname) + '*')
+        for of in outfiles:
+            _log.info("Copying preserved copy of '{0}' into '{1}'".format(
+                of, build_dir))
+            shutil.copy2(of, build_dir)
+
     # make figures
     try:
         results = render_figures(code,
@@ -728,7 +793,8 @@ def run(arguments, content, options, state_machine, state, lineno):
                                  function_name,
                                  config,
                                  context_reset=context_opt == 'reset',
-                                 close_figs=context_opt == 'close-figs')
+                                 close_figs=context_opt == 'close-figs',
+                                 outname=outname)
         errors = []
     except PlotError as err:
         reporter = state.memo.reporter

diff --git a/lib/matplotlib/tests/tinypages/some_plots.rst b/lib/matplotlib/tests/tinypages/some_plots.rst
@@ -126,4 +126,11 @@ Plot 16 uses a specific function in a file with plot commands:
 
 .. plot:: range6.py range6
 
+Plot 17 has an outname
 
+.. plot::
+    :context: close-figs
+    :outname: plot17out
+
+    plt.figure()
+    plt.plot(range(4))