diff -r 654ec6ed3225 Doc/c-api/object.rst
--- a/Doc/c-api/object.rst	Thu Dec 15 09:14:25 2016 +0100
+++ b/Doc/c-api/object.rst	Thu Dec 15 09:34:31 2016 +0100
@@ -272,11 +272,20 @@ Object Protocol
 
    Call a callable Python object *callable*, with a variable number of C arguments.
    The C arguments are described using a :c:func:`Py_BuildValue` style format
-   string.  The format can be *NULL*, indicating that no arguments are provided.
+   string.
 
-   Returns the result of the call on success, or *NULL* on failure.
+   If *format* is ``"O"`` and the argument is a tuple, the tuple is unpacked as
+   ``callable(*arg)``. Use the format string ``"(O)"`` to avoid unpacking if
+   there is a single argument.
 
-   This is the equivalent of the Python expression: ``callable(*args)``.
+   The format can be *NULL*, indicating that no arguments are provided.
+
+   Returns the result of the call on success, or raise an exception and return
+   *NULL* on failure.
+
+   This is the equivalent of the Python expression: ``callable(arg1, arg2,
+   ...)``, or ``callable(*arg)`` if *format* is ``"O"`` and the argument is
+   a tuple.
 
    Note that if you only pass :c:type:`PyObject \*` args,
    :c:func:`PyObject_CallFunctionObjArgs` is a faster alternative.
diff -r 654ec6ed3225 Include/abstract.h
--- a/Include/abstract.h	Thu Dec 15 09:14:25 2016 +0100
+++ b/Include/abstract.h	Thu Dec 15 09:34:31 2016 +0100
@@ -367,16 +367,21 @@ PyAPI_FUNC(PyObject *) _Py_CheckFunction
 PyAPI_FUNC(PyObject *) PyObject_CallObject(PyObject *callable,
                                            PyObject *args);
 
-/* Call a callable Python object, callable, with a variable number of C
-   arguments. The C arguments are described using a mkvalue-style format
-   string.
+/* Call a callable Python object 'callable' with a variable number of C
+   arguments. The C arguments are described using a Py_BuildValue() style
+   format string.
+
+   If 'format' is "O" and the argument is a tuple, the tuple is unpacked as
+   callable(*arg). Use the format string "(O)" to avoid unpacking if there is a
+   single argument.
 
    The format may be NULL, indicating that no arguments are provided.
 
-   Returns the result of the call on success, or NULL on failure.
+   Returns the result of the call on success, or raise an exception and return
+   NULL on failure.
 
-   This is the equivalent of the Python expression:
-   callable(arg1, arg2, ...). */
+   This is the equivalent of the Python expression: callable(arg1, arg2, ...),
+   or callable(*arg) if format is "O" and the argument is a tuple. */
 PyAPI_FUNC(PyObject *) PyObject_CallFunction(PyObject *callable,
                                              const char *format, ...);