diff -r 3ab32f7add6e Doc/library/contextlib.rst
--- a/Doc/library/contextlib.rst	Fri Aug 19 18:59:15 2016 +0200
+++ b/Doc/library/contextlib.rst	Sat Aug 20 17:02:00 2016 +0200
@@ -107,7 +107,7 @@
    ``page.close()`` will be called when the :keyword:`with` block is exited.
 
 
-.. function:: suppress(*exceptions)
+.. function:: suppress(*exceptions, unless=None)
 
    Return a context manager that suppresses any of the specified exceptions
    if they occur in the body of a with statement and then resumes execution
@@ -118,6 +118,14 @@
    silently continuing with program execution is known to be the right
    thing to do.
 
+   A whitelist of exceptions that will not suppressed can also be specified
+   as one exception or a tuple of exceptions to the *unless* keyword
+   argument.
+   Any whitelisted exception will not be suppressed.
+   Such whitelisted exceptions should normally be subclasses of at least one
+   of the suppressed exceptions for this operation to make sense. But that
+   is not enforced.
+
    For example::
 
        from contextlib import suppress
@@ -125,7 +133,7 @@
        with suppress(FileNotFoundError):
            os.remove('somefile.tmp')
 
-       with suppress(FileNotFoundError):
+       with suppress(OSError, unless=FileNotFoundError):
            os.remove('someotherfile.tmp')
 
    This code is equivalent to::
@@ -138,12 +146,16 @@
        try:
            os.remove('someotherfile.tmp')
        except FileNotFoundError:
+           raise
+       except OSError:
            pass
 
    This context manager is :ref:`reentrant <reentrant-cms>`.
 
    .. versionadded:: 3.4
 
+   .. versionchanged:: 3.6
+      The *unless* keyword argument was added.
 
 .. function:: redirect_stdout(new_target)
 
diff -r 3ab32f7add6e Lib/contextlib.py
--- a/Lib/contextlib.py	Fri Aug 19 18:59:15 2016 +0200
+++ b/Lib/contextlib.py	Sat Aug 20 17:02:00 2016 +0200
@@ -234,10 +234,38 @@
          with suppress(FileNotFoundError):
              os.remove(somefile)
          # Execution still resumes here if the file was already removed
+
+    A whitelist of exceptions that will not suppressed can also be specified
+    as one exception or a tuple of exceptions to the 'unless' keyword
+    argument.
+    Any whitelisted exception will not be suppressed, even if it is a subclass
+    of one of the supplied exceptions to be suppressed.
+    Such whitelisted exceptions should normally be subclasses of at least one
+    of the suppressed exceptions for this operation to make sense. But that
+    is not enforced.
+
+         try:
+             with suppress(OSError, unless=PermissionError):
+                 os.remove(somefile)
+             # Execution still resumes here for any OSError,
+             # except for PermissionError.
+         except PermissionError:
+             # Execution resumes here for PermissionError.
+             pass
+
+         try:
+             with suppress(OSError, unless=(PermissionError, FileNotFoundError)):
+                 os.remove(somefile)
+             # Execution still resumes here for any OSError,
+             # except for PermissionError and FileNotFoundError.
+         except (PermissionError, FileNotFoundError):
+             # Execution resumes here for PermissionError and FileNotFoundError.
+             pass
     """
 
-    def __init__(self, *exceptions):
+    def __init__(self, *exceptions, unless=None):
         self._exceptions = exceptions
+        self._unless = unless or ()
 
     def __enter__(self):
         pass
@@ -252,7 +280,9 @@
         # exactly reproduce the limitations of the CPython interpreter.
         #
         # See http://bugs.python.org/issue12029 for more details
-        return exctype is not None and issubclass(exctype, self._exceptions)
+        return exctype is not None and \
+               issubclass(exctype, self._exceptions) and \
+               not issubclass(exctype, self._unless)
 
 
 # Inspired by discussions on http://bugs.python.org/issue13585
diff -r 3ab32f7add6e Lib/test/test_contextlib.py
--- a/Lib/test/test_contextlib.py	Fri Aug 19 18:59:15 2016 +0200
+++ b/Lib/test/test_contextlib.py	Sat Aug 20 17:02:00 2016 +0200
@@ -953,5 +953,30 @@
             1/0
         self.assertTrue(outer_continued)
 
+    def test_unless(self):
+        with self.assertRaises(ZeroDivisionError):
+            with suppress(Exception, unless=ZeroDivisionError):
+                1/0
+        with suppress(Exception, unless=ZeroDivisionError):
+            len(5)
+        with self.assertRaises(ZeroDivisionError):
+            with suppress(ArithmeticError, TypeError, unless=ZeroDivisionError):
+                1/0
+        with suppress(ArithmeticError, TypeError, unless=TypeError):
+            1/0
+
+    def test_multiple_unless(self):
+        with self.assertRaises(ZeroDivisionError):
+            with suppress(Exception, unless=(ArithmeticError, TypeError)):
+                1/0
+        with self.assertRaises(TypeError):
+            with suppress(Exception, unless=(ArithmeticError, TypeError)):
+                len(5)
+        with suppress(Exception, unless=(IndexError, OSError)):
+            1/0
+        with suppress(Exception, unless=(IndexError, OSError)):
+            len(5)
+
+
 if __name__ == "__main__":
     unittest.main()