diff --git a/gnu/packages/patches/python-3-search-paths.patch b/gnu/packages/patches/python-3-search-paths.patch
index 7feddb8e30..73e3f4ccf5 100644
--- a/gnu/packages/patches/python-3-search-paths.patch
+++ b/gnu/packages/patches/python-3-search-paths.patch
@@ -3,17 +3,14 @@ looking for headers and libraries.
 
 --- setup.py	2015-10-07 23:32:58.891329173 +0200
 +++ setup.py	2015-10-07 23:46:29.653349924 +0200
-@@ -507,11 +507,8 @@ class PyBuildExt(build_ext):
+@@ -575,8 +575,8 @@
          # if a file is found in one of those directories, it can
          # be assumed that no additional -I,-L directives are needed.
          if not cross_compiling:
--            lib_dirs = self.compiler.library_dirs + [
--                '/lib64', '/usr/lib64',
--                '/lib', '/usr/lib',
--                ]
--            inc_dirs = self.compiler.include_dirs + ['/usr/include']
+-            lib_dirs = self.compiler.library_dirs + system_lib_dirs
+-            inc_dirs = self.compiler.include_dirs + system_include_dirs
 +            lib_dirs = os.getenv('LIBRARY_PATH', '').split(os.pathsep)
 +            inc_dirs = os.getenv('C_INCLUDE_PATH', '').split(os.pathsep)
          else:
-             lib_dirs = self.compiler.library_dirs[:]
-             inc_dirs = self.compiler.include_dirs[:]
+             # Add the sysroot paths. 'sysroot' is a compiler option used to
+             # set the logical path of the standard system headers and
diff --git a/gnu/packages/python.scm b/gnu/packages/python.scm
index dbb5ccb52e..82639939fd 100644
--- a/gnu/packages/python.scm
+++ b/gnu/packages/python.scm
@@ -338,7 +338,7 @@ (define-public python-2 python-2.7)
 
 (define-public python-3.6
   (package (inherit python-2)
-    (version "3.6.3")
+    (version "3.6.4")
     (source (origin
               (method url-fetch)
               (uri (string-append "https://www.python.org/ftp/python/"
@@ -351,17 +351,13 @@ (define-public python-3.6
               (patch-flags '("-p0"))
               (sha256
                (base32
-                "1nl1raaagr4car787a2hmjv2dw6gqny53xfd6wisbgx4r5kxk9yd"))
+                "1fna7g8jxzl4kd2pqmmqhva5724c5m920x3fsrpsgskaylmr76qm"))
               (snippet
                '(begin
                   (for-each delete-file
                             '("Lib/ctypes/test/test_structures.py" ; fails on aarch64
                               "Lib/ctypes/test/test_win32.py" ; fails on aarch64
-                              "Lib/test/test_fcntl.py" ; fails on aarch64
-                              ;; This test fails on kernels older than 4.5.
-                              ;; It is skipped on these kernels in later
-                              ;; versions of Python.
-                              "Lib/test/test_socket.py"))
+                              "Lib/test/test_fcntl.py")) ; fails on aarch64
                   #t))))
     (arguments
      (substitute-keyword-arguments (package-arguments python-2)