diff --git a/doc/api/next_api_changes/2019-06-05-JKS.rst b/doc/api/next_api_changes/2019-06-05-JKS.rst
@@ -0,0 +1,10 @@
+Removals
+````````
+
+The following members of ``matplotlib.backends.backend_pdf.PdfFile`` were removed:
+
+- ``nextObject``
+- ``nextFont``
+- ``nextAlphaState``
+- ``nextHatch``
+- ``nextImage``
diff --git a/lib/matplotlib/backends/backend_pdf.py b/lib/matplotlib/backends/backend_pdf.py
@@ -8,10 +8,10 @@
 from datetime import datetime
 from functools import total_ordering
 from io import BytesIO
+import itertools
 import logging
 import math
 import os
-import pathlib
 import re
 import struct
 import time
@@ -90,7 +90,7 @@
 # * encoding of fonts, including mathtext fonts and unicode support
 # * TTF support has lots of small TODOs, e.g., how do you know if a font
 #   is serif/sans-serif, or symbolic/non-symbolic?
-# * draw_markers, draw_line_collection, etc.
+# * draw_quad_mesh
 
 
 def fill(strings, linelen=75):
@@ -348,11 +348,22 @@ class Stream:
     __slots__ = ('id', 'len', 'pdfFile', 'file', 'compressobj', 'extra', 'pos')
 
     def __init__(self, id, len, file, extra=None, png=None):
-        """id: object id of stream; len: an unused Reference object for the
-        length of the stream, or None (to use a memory buffer); file:
-        a PdfFile; extra: a dictionary of extra key-value pairs to
-        include in the stream header; png: if the data is already
-        png compressed, the decode parameters"""
+        """
+        Parameters
+        ----------
+
+        id : int
+            Object id of the stream.
+        len : Reference or None
+            An unused Reference object for the length of the stream;
+            None means to use a memory buffer so the length can be inlined.
+        file : PdfFile
+            The underlying object to write the stream to.
+        extra : dict from Name to anything, or None
+            Extra key-value pairs to include in the stream header.
+        png : dict or None
+            If the data is already png encoded, the decode parameters.
+        """
         self.id = id            # object id
         self.len = len          # id of length object
         self.pdfFile = file
@@ -424,7 +435,25 @@ class PdfFile:
     """PDF file object."""
 
     def __init__(self, filename, metadata=None):
-        self.nextObject = 1     # next free object id
+        """
+        Parameters
+        ----------
+
+        filename : file-like object or string
+            Output target; if a string, a file will be opened for writing.
+        metadata : dict from strings to strings and dates
+            Information dictionary object (see PDF reference section 10.2.1
+            'Document Information Dictionary'), e.g.:
+            `{'Creator': 'My software', 'Author': 'Me',
+            'Title': 'Awesome fig'}`.
+
+            The standard keys are `'Title'`, `'Author'`, `'Subject'`,
+            `'Keywords'`, `'Creator'`, `'Producer'`, `'CreationDate'`,
+            `'ModDate'`, and `'Trapped'`. Values have been predefined
+            for `'Creator'`, `'Producer'` and `'CreationDate'`. They
+            can be removed by setting them to `None`.
+        """
+        self._object_seq = itertools.count(1)  # consumed by reserveObject
         self.xrefTable = [[0, 65535, 'the zero object']]
         self.passed_in_file_object = False
         self.original_file_like = None
@@ -482,21 +511,21 @@ def __init__(self, filename, metadata=None):
                          if v is not None}
 
         self.fontNames = {}     # maps filenames to internal font names
-        self.nextFont = 1       # next free internal font name
+        self._internal_font_seq = (Name(f'F{i}') for i in itertools.count(1))
         self.dviFontInfo = {}   # maps dvi font names to embedding information
         # differently encoded Type-1 fonts may share the same descriptor
         self.type1Descriptors = {}
         self.used_characters = {}
 
         self.alphaStates = {}   # maps alpha values to graphics state objects
-        self.nextAlphaState = 1
+        self._alpha_state_seq = (Name(f'A{i}') for i in itertools.count(1))
         # reproducible writeHatches needs an ordered dict:
         self.hatchPatterns = collections.OrderedDict()
-        self.nextHatch = 1
+        self._hatch_pattern_seq = (Name(f'H{i}') for i in itertools.count(1))
         self.gouraudTriangles = []
 
         self._images = collections.OrderedDict()   # reproducible writeImages
-        self.nextImage = 1
+        self._image_seq = (Name(f'I{i}') for i in itertools.count(1))
 
         self.markers = collections.OrderedDict()   # reproducible writeMarkers
         self.multi_byte_charprocs = {}
@@ -643,9 +672,8 @@ def fontName(self, fontprop):
 
         Fx = self.fontNames.get(filename)
         if Fx is None:
-            Fx = Name('F%d' % self.nextFont)
+            Fx = next(self._internal_font_seq)
             self.fontNames[filename] = Fx
-            self.nextFont += 1
             _log.debug('Assigning font %s = %r', Fx, filename)
 
         return Fx
@@ -669,8 +697,7 @@ def dviFontName(self, dvifont):
                 "the font may lack a Type-1 version"
                 .format(psfont.psname, dvifont.texname))
 
-        pdfname = Name('F%d' % self.nextFont)
-        self.nextFont += 1
+        pdfname = next(self._internal_font_seq)
         _log.debug('Assigning font %s = %s (dvi)', pdfname, dvifont.texname)
         self.dviFontInfo[dvifont.texname] = types.SimpleNamespace(
             dvifont=dvifont,
@@ -1186,8 +1213,7 @@ def alphaState(self, alpha):
         if state is not None:
             return state[0]
 
-        name = Name('A%d' % self.nextAlphaState)
-        self.nextAlphaState += 1
+        name = next(self._alpha_state_seq)
         self.alphaStates[alpha] = \
             (name, {'Type': Name('ExtGState'),
                     'CA': alpha[0], 'ca': alpha[1]})
@@ -1207,8 +1233,7 @@ def hatchPattern(self, hatch_style):
         if pattern is not None:
             return pattern
 
-        name = Name('H%d' % self.nextHatch)
-        self.nextHatch += 1
+        name = next(self._hatch_pattern_seq)
         self.hatchPatterns[hatch_style] = name
         return name
 
@@ -1300,9 +1325,8 @@ def imageObject(self, image):
         if entry is not None:
             return entry[1]
 
-        name = Name('I%d' % self.nextImage)
-        ob = self.reserveObject('image %d' % self.nextImage)
-        self.nextImage += 1
+        name = next(self._image_seq)
+        ob = self.reserveObject(f'image {name}')
         self._images[id(image)] = (image, name, ob)
         return name
 
@@ -1495,8 +1519,7 @@ def reserveObject(self, name=''):
         the object with writeObject.
         """
 
-        id = self.nextObject
-        self.nextObject += 1
+        id = next(self._object_seq)
         self.xrefTable.append([None, 0, name])
         return Reference(id)
 
@@ -1510,7 +1533,7 @@ def writeObject(self, object, contents):
     def writeXref(self):
         """Write out the xref table."""
         self.startxref = self.fh.tell() - self.tell_base
-        self.write(b"xref\n0 %d\n" % self.nextObject)
+        self.write(b"xref\n0 %d\n" % len(self.xrefTable))
         for i, (offset, generation, name) in enumerate(self.xrefTable):
             if offset is None:
                 raise AssertionError(
@@ -1557,7 +1580,7 @@ def writeTrailer(self):
 
         self.write(b"trailer\n")
         self.write(pdfRepr(
-            {'Size': self.nextObject,
+            {'Size': len(self.xrefTable),
              'Root': self.rootObject,
              'Info': self.infoObject}))
         # Could add 'ID'
@@ -2316,13 +2339,6 @@ def finalize(self):
             cmds.extend(self.pop())
         return cmds
 
-########################################################################
-#
-# The following functions and classes are for pylab and implement
-# window/figure managers, etc...
-#
-########################################################################
-
 
 class PdfPages:
     """