diff --git a/Doc/library/site.rst b/Doc/library/site.rst
index 2175c3e2e74..d93e938b5c9 100644
--- a/Doc/library/site.rst
+++ b/Doc/library/site.rst
@@ -38,6 +38,9 @@ Unix and Macintosh).  For each of the distinct head-tail combinations, it sees
 if it refers to an existing directory, and if so, adds it to ``sys.path`` and
 also inspects the newly added path for configuration files.
 
+.. deprecated:: 3.4
+   Support for the "site-python" directory will be removed in 3.5.
+
 If a file named "pyvenv.cfg" exists one directory above sys.executable,
 sys.prefix and sys.exec_prefix are set to that directory and
 it is also checked for site-packages and site-python (sys.base_prefix and
diff --git a/Doc/whatsnew/3.4.rst b/Doc/whatsnew/3.4.rst
index 392af3b3c57..6e261d5913d 100644
--- a/Doc/whatsnew/3.4.rst
+++ b/Doc/whatsnew/3.4.rst
@@ -685,7 +685,8 @@ Deprecated functions and types of the C API
 Deprecated features
 -------------------
 
-* No feature deprecations are planned for Python 3.4.
+* The site module adding a "site-python" directory to sys.path, if it
+  exists, is deprecated (:issue:`19375`).
 
 
 Porting to Python 3.4
diff --git a/Lib/site.py b/Lib/site.py
index bb329b43812..b0d8268f816 100644
--- a/Lib/site.py
+++ b/Lib/site.py
@@ -326,6 +326,11 @@ def addsitepackages(known_paths, prefixes=None):
     """Add site-packages (and possibly site-python) to sys.path"""
     for sitedir in getsitepackages(prefixes):
         if os.path.isdir(sitedir):
+            if "site-python" in sitedir:
+                import warnings
+                warnings.warn('"site-python" directories will not be '
+                              'supported in 3.5 anymore',
+                              DeprecationWarning)
             addsitedir(sitedir, known_paths)
 
     return known_paths
diff --git a/Lib/sre_compile.py b/Lib/sre_compile.py
index e08ec661aaa..e194aaace76 100644
--- a/Lib/sre_compile.py
+++ b/Lib/sre_compile.py
@@ -353,6 +353,27 @@ def _simple(av):
     lo, hi = av[2].getwidth()
     return lo == hi == 1 and av[2][0][0] != SUBPATTERN
 
+def _generate_overlap_table(prefix):
+    """
+    Generate an overlap table for the following prefix.
+    An overlap table is a table of the same size as the prefix which
+    informs about the potential self-overlap for each index in the prefix:
+    - if overlap[i] == 0, prefix[i:] can't overlap prefix[0:...]
+    - if overlap[i] == k with 0 < k <= i, prefix[i-k+1:i+1] overlaps with
+      prefix[0:k]
+    """
+    table = [0] * len(prefix)
+    for i in range(1, len(prefix)):
+        idx = table[i - 1]
+        while prefix[i] != prefix[idx]:
+            if idx == 0:
+                table[i] = 0
+                break
+            idx = table[idx - 1]
+        else:
+            table[i] = idx + 1
+    return table
+
 def _compile_info(code, pattern, flags):
     # internal: compile an info block.  in the current version,
     # this contains min/max pattern width, and an optional literal
@@ -449,12 +470,7 @@ def _compile_info(code, pattern, flags):
         emit(prefix_skip) # skip
         code.extend(prefix)
         # generate overlap table
-        table = [-1] + ([0]*len(prefix))
-        for i in range(len(prefix)):
-            table[i+1] = table[i]+1
-            while table[i+1] > 0 and prefix[i] != prefix[table[i+1]-1]:
-                table[i+1] = table[table[i+1]-1]+1
-        code.extend(table[1:]) # don't store first entry
+        code.extend(_generate_overlap_table(prefix))
     elif charset:
         _compile_charset(charset, flags, code)
     code[skip] = len(code) - skip
diff --git a/Lib/test/test_re.py b/Lib/test/test_re.py
index 5e685850653..9ee077da7b4 100644
--- a/Lib/test/test_re.py
+++ b/Lib/test/test_re.py
@@ -3,10 +3,12 @@ from test.support import verbose, run_unittest, gc_collect, bigmemtest, _2G, \
 import io
 import re
 from re import Scanner
+import sre_compile
 import sre_constants
 import sys
 import string
 import traceback
+import unittest
 from weakref import proxy
 
 # Misc tests from Tim Peters' re.doc
@@ -15,8 +17,6 @@ from weakref import proxy
 # what you're doing. Some of these tests were carefully modeled to
 # cover most of the code.
 
-import unittest
-
 class S(str):
     def __getitem__(self, index):
         return S(super().__getitem__(index))
@@ -1140,6 +1140,22 @@ class ReTests(unittest.TestCase):
                 self.assertEqual(m.group(1), "")
                 self.assertEqual(m.group(2), "y")
 
+
+class ImplementationTest(unittest.TestCase):
+    """
+    Test implementation details of the re module.
+    """
+
+    def test_overlap_table(self):
+        f = sre_compile._generate_overlap_table
+        self.assertEqual(f(""), [])
+        self.assertEqual(f("a"), [0])
+        self.assertEqual(f("abcd"), [0, 0, 0, 0])
+        self.assertEqual(f("aaaa"), [0, 1, 2, 3])
+        self.assertEqual(f("ababba"), [0, 0, 1, 2, 0, 1])
+        self.assertEqual(f("abcabdac"), [0, 0, 0, 1, 2, 0, 1, 0])
+
+
 def run_re_tests():
     from test.re_tests import tests, SUCCEED, FAIL, SYNTAX_ERROR
     if verbose:
@@ -1269,7 +1285,7 @@ def run_re_tests():
 
 
 def test_main():
-    run_unittest(ReTests)
+    run_unittest(__name__)
     run_re_tests()
 
 if __name__ == "__main__":
diff --git a/Misc/NEWS b/Misc/NEWS
index 5f6ccad7521..be64bee591d 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -27,6 +27,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #19375: The site module adding a "site-python" directory to sys.path,
+  if it exists, is now deprecated.
+
 - Issue #19379: Lazily import linecache in the warnings module, to make
   startup with warnings faster until a warning gets printed.