diff --git a/Doc/library/os.path.rst b/Doc/library/os.path.rst
index c85412e..6d177f8 100644
--- a/Doc/library/os.path.rst
+++ b/Doc/library/os.path.rst
@@ -23,10 +23,6 @@
    their parameters.  The result is an object of the same type, if a path or
    file name is returned.
 
-.. note::
-
-   On Windows, many of these functions do not properly support UNC pathnames.
-   :func:`splitunc` and :func:`ismount` do handle them correctly.
 
 .. note::
 
@@ -266,10 +262,20 @@
 .. function:: splitdrive(path)
 
    Split the pathname *path* into a pair ``(drive, tail)`` where *drive* is either
-   a drive specification or the empty string.  On systems which do not use drive
+   a mount point or the empty string.  On systems which do not use drive
    specifications, *drive* will always be the empty string.  In all cases, ``drive
    + tail`` will be the same as *path*.
 
+   On Windows, splits a pathname into drive/UNC sharepoint and relative path.
+
+   If the path contains a drive letter, drive will contain everything
+   up to and including the colon.
+   e.g. ``splitdrive("c:/dir")`` returns ``("c:", "/dir")``
+
+   If the path contains a UNC path, drive will contain the host name
+   and share, up to but not including the fourth separator.
+   e.g. ``splitdrive("//host/computer/dir")`` returns ``("//host/computer", "/dir")``
+
 
 .. function:: splitext(path)
 
@@ -281,6 +287,9 @@
 
 .. function:: splitunc(path)
 
+   .. deprecated:: 3.1
+      Use *splitdrive* instead.
+
    Split the pathname *path* into a pair ``(unc, rest)`` so that *unc* is the UNC
    mount point (such as ``r'\\host\mount'``), if present, and *rest* the rest of
    the path (such as  ``r'\path\file.ext'``).  For paths containing drive letters,
diff --git a/Lib/ntpath.py b/Lib/ntpath.py
index ac928e1..2fd26b1 100644
--- a/Lib/ntpath.py
+++ b/Lib/ntpath.py
@@ -34,6 +34,12 @@
     altsep = '/'
 devnull = 'nul'
 
+def _get_empty(path):
+    if isinstance(path, bytes):
+        return b''
+    else:
+        return ''
+
 def _get_sep(path):
     if isinstance(path, bytes):
         return b'\\'
@@ -76,9 +82,9 @@
 
 
 # Return whether a path is absolute.
-# Trivial in Posix, harder on the Mac or MS-DOS.
-# For DOS it is absolute if it starts with a slash or backslash (current
-# volume), or if a pathname after the volume letter and colon / UNC resource
+# Trivial in Posix, harder on Windows.
+# For Windows it is absolute if it starts with a slash or backslash (current
+# volume), or if a pathname after the volume-letter-and-colon or UNC-resource
 # starts with a slash or backslash.
 
 def isabs(s):
@@ -104,22 +110,40 @@
 
         elif isabs(b):
             # This probably wipes out path so far.  However, it's more
-            # complicated if path begins with a drive letter:
+            # complicated if path begins with a drive letter.  You get a+b
+            # (minus redundant slashes) in these four cases:
             #     1. join('c:', '/a') == 'c:/a'
-            #     2. join('c:/', '/a') == 'c:/a'
-            # But
-            #     3. join('c:/a', '/b') == '/b'
-            #     4. join('c:', 'd:/') = 'd:/'
-            #     5. join('c:/', 'd:/') = 'd:/'
-            if path[1:2] != colon or b[1:2] == colon:
-                # Path doesn't start with a drive letter, or cases 4 and 5.
-                b_wins = 1
+            #     2. join('//computer/share', '/a') == '//computer/share/a'
+            #     3. join('c:/', '/a') == 'c:/a'
+            #     4. join('//computer/share/', '/a') == '//computer/share/a'
+            # But b wins in all of these cases:
+            #     5. join('c:/a', '/b') == '/b'
+            #     6. join('//computer/share/a', '/b') == '/b'
+            #     7. join('c:', 'd:/') == 'd:/'
+            #     8. join('c:', '//computer/share/') == '//computer/share/'
+            #     9. join('//computer/share', 'd:/') == 'd:/'
+            #    10. join('//computer/share', '//computer/share/') == '//computer/share/'
+            #    11. join('c:/', 'd:/') == 'd:/'
+            #    12. join('c:/', '//computer/share/') == '//computer/share/'
+            #    13. join('//computer/share/', 'd:/') == 'd:/'
+            #    14. join('//computer/share/', '//computer/share/') == '//computer/share/'
+            b_prefix, b_rest = splitdrive(b)
 
-            # Else path has a drive letter, and b doesn't but is absolute.
-            elif len(path) > 3 or (len(path) == 3 and
-                                   path[-1:] not in seps):
-                # case 3
+            # if b has a prefix, it always wins.
+            if b_prefix:
                 b_wins = 1
+            else:
+                # b doesn't have a prefix.
+                # but isabs(b) returned true.
+                # and therefore b_rest[0] must be a slash.
+                # (but let's check that.)
+                assert(b_rest and b_rest[0] in seps)
+
+                # so, b still wins if path has a rest that's more than a sep.
+                # you get a+b if path_rest is empty or only has a sep.
+                # (see cases 1-4 for times when b loses.)
+                path_rest = splitdrive(path)[1]
+                b_wins = path_rest and path_rest not in seps
 
         if b_wins:
             path = b
@@ -152,22 +176,64 @@
 # colon) and the path specification.
 # It is always true that drivespec + pathspec == p
 def splitdrive(p):
-    """Split a pathname into drive and path specifiers. Returns a 2-tuple
-"(drive,path)";  either part may be empty"""
-    if p[1:2] == _get_colon(p):
-        return p[0:2], p[2:]
-    return p[:0], p
+    """Split a pathname into drive/UNC sharepoint and relative path specifiers.
+    Returns a 2-tuple (drive_or_unc, path); either part may be empty.
+
+    If you assign
+        result = splitdrive(p)
+    It is always true that:
+        result[0] + result[1] == p
+
+    If the path contained a drive letter, drive_or_unc will contain everything
+    up to and including the colon.  e.g. splitdrive("c:/dir") returns ("c:", "/dir")
+
+    If the path contained a UNC path, the drive_or_unc will contain the host name
+    and share up to but not including the fourth directory separator character.
+    e.g. splitdrive("//host/computer/dir") returns ("//host/computer", "/dir")
+
+    Paths cannot contain both a drive letter and a UNC path.
+
+    """
+    empty = _get_empty(p)
+    if len(p) > 1:
+        sep = _get_sep(p)
+        normp = normcase(p)
+        if (normp[0:2] == sep*2) and (normp[2:3] != sep):
+            # is a UNC path:
+            # vvvvvvvvvvvvvvvvvvvv drive letter or UNC path
+            # \\machine\mountpoint\directory\etc\...
+            #           directory ^^^^^^^^^^^^^^^
+            index = normp.find(sep, 2)
+            if index == -1:
+                return empty, p
+            index2 = normp.find(sep, index + 1)
+            # a UNC path can't have two slashes in a row
+            # (after the initial two)
+            if index2 == index + 1:
+                return empty, p
+            if index2 == -1:
+                index2 = len(p)
+            return p[:index2], p[index2:]
+        if normp[1:2] == _get_colon(p):
+            return p[:2], p[2:]
+    return empty, p
 
 
 # Parse UNC paths
 def splitunc(p):
-    """Split a pathname into UNC mount point and relative path specifiers.
+    """Deprecated since Python 3.1.  Please use splitdrive() instead;
+    it now handles UNC paths.
+
+    Split a pathname into UNC mount point and relative path specifiers.
 
     Return a 2-tuple (unc, rest); either part may be empty.
     If unc is not empty, it has the form '//host/mount' (or similar
     using backslashes).  unc+rest is always the input path.
     Paths containing drive letters never have an UNC part.
     """
+    import warnings
+    warnings.warn("ntpath.splitunc is deprecated, use ntpath.splitdrive instead",
+                  PendingDeprecationWarning)
     sep = _get_sep(p)
     if not p[1:2]:
         return p[:0], p # Drive letter present
@@ -256,12 +322,11 @@
 
 def ismount(path):
     """Test whether a path is a mount point (defined as root of drive)"""
-    unc, rest = splitunc(path)
     seps = _get_bothseps(path)
-    if unc:
-        return rest in p[:0] + seps
-    p = splitdrive(path)[1]
-    return len(p) == 1 and p[0] in seps
+    root, rest = splitdrive(path)
+    if root and root[0] in seps:
+        return (not rest) or (rest in seps)
+    return rest in seps
 
 
 # Expand paths beginning with '~' or '~user'.
@@ -445,25 +510,12 @@
     dotdot = _get_dot(path) * 2
     path = path.replace(_get_altsep(path), sep)
     prefix, path = splitdrive(path)
-    # We need to be careful here. If the prefix is empty, and the path starts
-    # with a backslash, it could either be an absolute path on the current
-    # drive (\dir1\dir2\file) or a UNC filename (\\server\mount\dir1\file). It
-    # is therefore imperative NOT to collapse multiple backslashes blindly in
-    # that case.
-    # The code below preserves multiple backslashes when there is no drive
-    # letter. This means that the invalid filename \\\a\b is preserved
-    # unchanged, where a\\\b is normalised to a\b. It's not clear that there
-    # is any better behaviour for such edge cases.
-    if not prefix:
-        # No drive letter - preserve initial backslashes
-        while path[:1] == sep:
-            prefix = prefix + sep
-            path = path[1:]
-    else:
-        # We have a drive letter - collapse initial backslashes
-        if path.startswith(sep):
-            prefix = prefix + sep
-            path = path.lstrip(sep)
+
+    # collapse initial backslashes
+    if path.startswith(sep):
+        prefix = prefix + sep
+        path = path.lstrip(sep)
+
     comps = path.split(sep)
     i = 0
     while i < len(comps):
@@ -528,22 +580,23 @@
 
     if not path:
         raise ValueError("no path specified")
-    start_list = abspath(start).split(sep)
-    path_list = abspath(path).split(sep)
-    if start_list[0].lower() != path_list[0].lower():
-        unc_path, rest = splitunc(path)
-        unc_start, rest = splitunc(start)
-        if bool(unc_path) ^ bool(unc_start):
-            raise ValueError("Cannot mix UNC and non-UNC paths (%s and %s)"
-                                                                % (path, start))
-        else:
-            raise ValueError("path is on drive %s, start on drive %s"
-                                                % (path_list[0], start_list[0]))
+
+    start_abs = abspath(normpath(start))
+    path_abs = abspath(normpath(path))
+    start_drive, start_rest = splitdrive(start_abs)
+    path_drive, path_rest = splitdrive(path_abs)
+    if start_drive != path_drive:
+        error = "path is on mount '{0}', start on mount '{1}'".format(
+            path_drive, start_drive)
+        raise ValueError(error)
+
+    start_list = [x for x in start_rest.split(sep) if x]
+    path_list = [x for x in path_rest.split(sep) if x]
     # Work out how much of the filepath is shared by start and path.
-    for i in range(min(len(start_list), len(path_list))):
-        if start_list[i].lower() != path_list[i].lower():
+    i = 0
+    for e1, e2 in zip(start_list, path_list):
+        if e1 != e2:
             break
-    else:
         i += 1
 
     if isinstance(path, bytes):
diff --git a/Lib/test/test_ntpath.py b/Lib/test/test_ntpath.py
index 2b2b7d5..4a7a48b 100644
--- a/Lib/test/test_ntpath.py
+++ b/Lib/test/test_ntpath.py
@@ -30,6 +30,7 @@
         raise TestFailed("%s should return: %s but returned: %s" \
               %(str(fn), str(wantResult), repr(gotResult)))
 
+
 class TestNtpath(unittest.TestCase):
     def test_splitext(self):
         tester('ntpath.splitext("foo.ext")', ('foo', '.ext'))
@@ -48,12 +49,18 @@
                ('c:', '\\foo\\bar'))
         tester('ntpath.splitdrive("c:/foo/bar")',
                ('c:', '/foo/bar'))
-
-    def test_splitunc(self):
-        tester('ntpath.splitunc("\\\\conky\\mountpoint\\foo\\bar")',
+        tester('ntpath.splitdrive("\\\\conky\\mountpoint\\foo\\bar")',
                ('\\\\conky\\mountpoint', '\\foo\\bar'))
-        tester('ntpath.splitunc("//conky/mountpoint/foo/bar")',
+        tester('ntpath.splitdrive("//conky/mountpoint/foo/bar")',
                ('//conky/mountpoint', '/foo/bar'))
+        tester('ntpath.splitdrive("\\\\\\conky\\mountpoint\\foo\\bar")',
+            ('', '\\\\\\conky\\mountpoint\\foo\\bar'))
+        tester('ntpath.splitdrive("///conky/mountpoint/foo/bar")',
+            ('', '///conky/mountpoint/foo/bar'))
+        tester('ntpath.splitdrive("\\\\conky\\\\mountpoint\\foo\\bar")',
+               ('', '\\\\conky\\\\mountpoint\\foo\\bar'))
+        tester('ntpath.splitdrive("//conky//mountpoint/foo/bar")',
+               ('', '//conky//mountpoint/foo/bar'))
 
     def test_split(self):
         tester('ntpath.split("c:\\foo\\bar")', ('c:\\foo', 'bar'))
@@ -62,10 +69,10 @@
 
         tester('ntpath.split("c:\\")', ('c:\\', ''))
         tester('ntpath.split("\\\\conky\\mountpoint\\")',
-               ('\\\\conky\\mountpoint', ''))
+               ('\\\\conky\\mountpoint\\', ''))
 
         tester('ntpath.split("c:/")', ('c:/', ''))
-        tester('ntpath.split("//conky/mountpoint/")', ('//conky/mountpoint', ''))
+        tester('ntpath.split("//conky/mountpoint/")', ('//conky/mountpoint/', ''))
 
     def test_isabs(self):
         tester('ntpath.isabs("c:\\")', 1)
@@ -116,6 +123,33 @@
         tester("ntpath.join('a\\', '')", 'a\\')
         tester("ntpath.join('a\\', '', '', '', '')", 'a\\')
 
+        # from comment in ntpath.join
+        tester("ntpath.join('c:', '/a')", 'c:/a')
+        tester("ntpath.join('//computer/share', '/a')", '//computer/share/a')
+        tester("ntpath.join('c:/', '/a')", 'c:/a')
+        tester("ntpath.join('//computer/share/', '/a')", '//computer/share/a')
+        tester("ntpath.join('c:/a', '/b')", '/b')
+        tester("ntpath.join('//computer/share/a', '/b')", '/b')
+        tester("ntpath.join('c:', 'd:/')", 'd:/')
+        tester("ntpath.join('c:', '//computer/share/')", '//computer/share/')
+        tester("ntpath.join('//computer/share', 'd:/')", 'd:/')
+        tester("ntpath.join('//computer/share', '//computer/share/')", '//computer/share/')
+        tester("ntpath.join('c:/', 'd:/')", 'd:/')
+        tester("ntpath.join('c:/', '//computer/share/')", '//computer/share/')
+        tester("ntpath.join('//computer/share/', 'd:/')", 'd:/')
+        tester("ntpath.join('//computer/share/', '//computer/share/')", '//computer/share/')
+
+        tester("ntpath.join('c:', '//computer/share/')", '//computer/share/')
+        tester("ntpath.join('c:/', '//computer/share/')", '//computer/share/')
+        tester("ntpath.join('c:/', '//computer/share/a/b')", '//computer/share/a/b')
+
+        tester("ntpath.join('\\\\computer\\share\\', 'a', 'b')", '\\\\computer\\share\\a\\b')
+        tester("ntpath.join('\\\\computer\\share', 'a', 'b')", '\\\\computer\\share\\a\\b')
+        tester("ntpath.join('\\\\computer\\share', 'a\\b')", '\\\\computer\\share\\a\\b')
+        tester("ntpath.join('//computer/share/', 'a', 'b')", '//computer/share/a\\b')
+        tester("ntpath.join('//computer/share', 'a', 'b')", '//computer/share\\a\\b')
+        tester("ntpath.join('//computer/share', 'a/b')", '//computer/share\\a/b')
+
     def test_normpath(self):
         tester("ntpath.normpath('A//////././//.//B')", r'A\B')
         tester("ntpath.normpath('A/./B')", r'A\B')
@@ -174,10 +208,9 @@
         # from any platform.
         try:
             import nt
+            tester('ntpath.abspath("C:\\")', "C:\\")
         except ImportError:
             pass
-        else:
-            tester('ntpath.abspath("C:\\")', "C:\\")
 
     def test_relpath(self):
         currentdir = os.path.split(os.getcwd())[-1]
@@ -188,8 +221,18 @@
         tester('ntpath.relpath("a", "../b")', '..\\'+currentdir+'\\a')
         tester('ntpath.relpath("a/b", "../c")', '..\\'+currentdir+'\\a\\b')
         tester('ntpath.relpath("a", "b/c")', '..\\..\\a')
+        tester('ntpath.relpath("c:/foo/bar/bat", "c:/x/y")', '..\\..\\foo\\bar\\bat')
         tester('ntpath.relpath("//conky/mountpoint/a", "//conky/mountpoint/b/c")', '..\\..\\a')
         tester('ntpath.relpath("a", "a")', '.')
+        tester('ntpath.relpath("/foo/bar/bat", "/x/y/z")', '..\\..\\..\\foo\\bar\\bat')
+        tester('ntpath.relpath("/foo/bar/bat", "/foo/bar")', 'bat')
+        tester('ntpath.relpath("/foo/bar/bat", "/")', 'foo\\bar\\bat')
+        tester('ntpath.relpath("/", "/foo/bar/bat")', '..\\..\\..')
+        tester('ntpath.relpath("/foo/bar/bat", "/x")', '..\\foo\\bar\\bat')
+        tester('ntpath.relpath("/x", "/foo/bar/bat")', '..\\..\\..\\x')
+        tester('ntpath.relpath("/", "/")', '.')
+        tester('ntpath.relpath("/a", "/a")', '.')
+        tester('ntpath.relpath("/a/b", "/a/b")', '.')
 
 
 def test_main():
diff --git a/Misc/NEWS b/Misc/NEWS
index 45d9a49..35490d2 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,10 @@
 Core and Builtins
 -----------------
 
+- Issue #5799: ntpath (ie, os.path on Windows) fully supports UNC pathnames
+  in all operations, including splitdrive, split, etc.  splitunc() now issues
+  a PendingDeprecation warning.
+
 - Issue #5920: For float.__format__, change the behavior with the
   empty presentation type (that is, not one of 'e', 'f', 'g', or 'n')
   to be like 'g' but with at least one decimal point and with a