diff --git a/requests/utils.py b/requests/utils.py
index a773f109..f4f98c45 100644
--- a/requests/utils.py
+++ b/requests/utils.py
@@ -396,6 +396,28 @@ def stream_decompress(iterator, mode='gzip'):
         if rv:
             yield rv
 
+# The unreserved URI characters (RFC 3986)
+UNRESERVED_SET = frozenset(
+    "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
+    + "0123456789-._~")
+
+def unquote_unreserved(uri):
+    """Un-escape any percent-escape sequences in a URI that are unreserved
+    characters.
+    This leaves all reserved, illegal and non-ASCII bytes encoded.
+    """
+    parts = uri.split('%')
+    for i in range(1, len(parts)):
+        h = parts[i][0:2]
+        if len(h) == 2:
+            c = chr(int(h, 16))
+            if c in UNRESERVED_SET:
+                parts[i] = c + parts[i][2:]
+            else:
+                parts[i] = '%' + parts[i]
+        else:
+            parts[i] = '%' + parts[i]
+    return ''.join(parts)
 
 def requote_path(path):
     """Re-quote the given URL path component.
@@ -404,5 +426,9 @@ def requote_path(path):
     ensure that it is fully and consistently quoted.
     """
     parts = path.split("/")
-    parts = (quote(unquote(part), safe="") for part in parts)
+    # Unquote only the unreserved characters
+    # Then quote only illegal characters (do not quote reserved, unreserved,
+    # or '%')
+    parts = (quote(unquote_unreserved(part), safe="!#$%&'()*+,/:;=?@[]~")
+             for part in parts)
     return "/".join(parts)