diff --git a/Lib/zipfile.py b/Lib/zipfile.py
index 8b99c11..5dc6516 100644
--- a/Lib/zipfile.py
+++ b/Lib/zipfile.py
@@ -16,6 +16,8 @@
 import sys
 import threading
 import time
+import contextlib
+from collections import OrderedDict
 
 try:
     import zlib # We may need its compression method
@@ -2182,6 +2184,79 @@
         path, tail = posixpath.split(path)
 
 
+class CompleteDirs(ZipFile):
+    """
+    A ZipFile subclass that ensures that implied directories
+    are always included in the namelist.
+    """
+
+    @staticmethod
+    def _implied_dirs(names):
+        parents = itertools.chain.from_iterable(map(_parents, names))
+        # Deduplicate entries in original order
+        implied_dirs = OrderedDict.fromkeys(
+            p + posixpath.sep for p in parents
+            # Cast names to a set for O(1) lookups
+            if p + posixpath.sep not in set(names)
+        )
+        return implied_dirs
+
+    def namelist(self):
+        names = super(CompleteDirs, self).namelist()
+        return names + list(self._implied_dirs(names))
+
+    def _name_set(self):
+        return set(self.namelist())
+
+    def resolve_dir(self, name):
+        """
+        If the name represents a directory, return that name
+        as a directory (with the trailing slash).
+        """
+        names = self._name_set()
+        dirname = name + '/'
+        dir_match = name not in names and dirname in names
+        return dirname if dir_match else name
+
+    @classmethod
+    def make(cls, source):
+        """
+        Given a source (filename or zipfile), return an
+        appropriate CompleteDirs subclass.
+        """
+        if isinstance(source, CompleteDirs):
+            return source
+
+        if not isinstance(source, ZipFile):
+            return cls(source)
+
+        # Only allow for FastPath when supplied zipfile is read-only
+        if 'r' not in source.mode:
+            cls = CompleteDirs
+
+        res = cls.__new__(cls)
+        vars(res).update(vars(source))
+        return res
+
+
+class FastLookup(CompleteDirs):
+    """
+    ZipFile subclass to ensure implicit
+    dirs exist and are resolved rapidly.
+    """
+    def namelist(self):
+        with contextlib.suppress(AttributeError):
+            return self.__names
+        self.__names = super(FastLookup, self).namelist()
+        return self.__names
+
+    def _name_set(self):
+        with contextlib.suppress(AttributeError):
+            return self.__lookup
+        self.__lookup = super(FastLookup, self)._name_set()
+        return self.__lookup
+
+
 class Path:
     """
     A pathlib-compatible interface for zip files.
@@ -2250,7 +2325,7 @@
     __repr = "{self.__class__.__name__}({self.root.filename!r}, {self.at!r})"
 
     def __init__(self, root, at=""):
-        self.root = root if isinstance(root, ZipFile) else ZipFile(root)
+        self.root = FastLookup.make(root)
         self.at = at
 
     @property
@@ -2282,12 +2357,12 @@
         return not self.is_dir()
 
     def exists(self):
-        return self.at in self._names()
+        return self.at in self.root._name_set()
 
     def iterdir(self):
         if not self.is_dir():
             raise ValueError("Can't listdir a file")
-        subs = map(self._next, self._names())
+        subs = map(self._next, self.root.namelist())
         return filter(self._is_child, subs)
 
     def __str__(self):
@@ -2298,25 +2373,10 @@
 
     def joinpath(self, add):
         next = posixpath.join(self.at, add)
-        next_dir = posixpath.join(self.at, add, "")
-        names = self._names()
-        return self._next(next_dir if next not in names and next_dir in names else next)
+        return self._next(self.root.resolve_dir(next))
 
     __truediv__ = joinpath
 
-    @staticmethod
-    def _implied_dirs(names):
-        return _unique_everseen(
-            parent + "/"
-            for name in names
-            for parent in _parents(name)
-            if parent + "/" not in names
-        )
-
-    @classmethod
-    def _add_implied_dirs(cls, names):
-        return names + list(cls._implied_dirs(names))
-
     @property
     def parent(self):
         parent_at = posixpath.dirname(self.at.rstrip('/'))
@@ -2324,9 +2384,6 @@
             parent_at += '/'
         return self._next(parent_at)
 
-    def _names(self):
-        return self._add_implied_dirs(self.root.namelist())
-
 
 def main(args=None):
     import argparse
@@ -2388,5 +2445,6 @@
                     zippath = ''
                 addToZip(zf, path, zippath)
 
+
 if __name__ == "__main__":
     main()