diff --git a/pep-0503.txt b/pep-0503.txt
index 09f737ed4..3b7087113 100644
--- a/pep-0503.txt
+++ b/pep-0503.txt
@@ -26,14 +26,14 @@ behavior for any implementation of the simple repository API.
 Specification
 =============
 
-A repository that implements the simple API is defined by its base url, this is
-the top level URL that all additional URLS are below. The API is named the
-"simple" repository due to fact that PyPI's base URL is
-``https://pypi.python.org/simple/``.
+A repository that implements the simple API is defined by its base URL, this is
+the top level URL that all additional URLs are below. The API is named the
+"simple" repository due to the fact that PyPI's base URL is
+``https://pypi.org/simple/``.
 
 .. note:: All subsequent URLs in this document will be relative to this base
           URL (so given PyPI's URL, an URL of ``/foo/`` would be
-          ``https://pypi.python.org/simple/foo/``.
+          ``https://pypi.org/simple/foo/``.
 
 
 Within a repository, the root URL (``/``) **MUST** be a valid HTML5 page with a
@@ -70,7 +70,7 @@ In addition to the above, the following constraints are placed on the API:
 * URLs may be either absolute or relative as long as they point to the correct
   location.
 
-* There is no constraints on where the files must be hosted relative to the
+* There are no constraints on where the files must be hosted relative to the
   repository.
 
 * There may be any other HTML elements on the API pages as long as the required