diff --git a/Doc/c-api/long.rst b/Doc/c-api/long.rst
index f592cb6..f50680b 100644
--- a/Doc/c-api/long.rst
+++ b/Doc/c-api/long.rst
@@ -85,13 +85,12 @@
    Return a new :c:type:`PyLongObject` based on the string value in *str*, which
    is interpreted according to the radix in *base*.  If *pend* is non-*NULL*,
    *\*pend* will point to the first character in *str* which follows the
-   representation of the number.  If *base* is ``0``, the radix will be
-   determined based on the leading characters of *str*: if *str* starts with
-   ``'0x'`` or ``'0X'``, radix 16 will be used; if *str* starts with ``'0o'`` or
-   ``'0O'``, radix 8 will be used; if *str* starts with ``'0b'`` or ``'0B'``,
-   radix 2 will be used; otherwise radix 10 will be used.  If *base* is not
-   ``0``, it must be between ``2`` and ``36``, inclusive.  Leading spaces are
-   ignored.  If there are no digits, :exc:`ValueError` will be raised.
+   representation of the number.  If *base* is ``0``, *str* is interpreted using
+   the :ref:`integers` definition; in this case, leading zeros in a
+   non-zero decimal number raises a :exc:`ValueError`. If *base* is not ``0``,
+   it must be between ``2`` and ``36``, inclusive.  Leading spaces and single
+   underscores after a base specifier and between digits are ignored.  If there
+   are no digits, :exc:`ValueError` will be raised.
 
 
 .. c:function:: PyObject* PyLong_FromUnicode(Py_UNICODE *u, Py_ssize_t length, int base)