Raymond Hettinger added the comment:

The docs are correct as-is.  This is a documented and tested behavior.

    >>> from heapq import nsmallest
    >>> list(nsmallest(3, ['larry', 'georg', 'raymond', 'guido', 'tim'], 
key=len))
    ['tim', 'larry', 'georg']

The C implementation doesn't have a key-argument.  That behavior gets added 
downstream in pure python in Lib/heapq.py which wraps the C-function and adds 
the additional behavior.

----------
assignee:  -> rhettinger
nosy: +rhettinger
priority: low -> normal
resolution:  -> invalid
status: open -> closed

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Python tracker <rep...@bugs.python.org>
<http://bugs.python.org/issue20407>
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