pythoncomplete is rather old and unmaintained.
Try to use Jedi: https://github.com/davidhalter/jedi-vim
It was originally an improved pythoncomplete, but is now much much more powerful!
It works for complex code:
And has additional features:

There is a list of all possible features:
- builtin functions/classes support
- complex module / function / class structures
- ignores syntax and indentation errors
- multiple returns / yields
- tuple assignments / array indexing / dictionary indexing
- exceptions / with-statement
- *args / **kwargs
- decorators
- descriptors -> property / staticmethod / classmethod
- closures
- generators (yield statement) / iterators
- support for some magic methods:
__call__,__iter__,__next__,
__get__,__getitem__,__init__ - support for list.append, set.add, list.extend, etc.
- (nested) list comprehensions / ternary expressions
- relative imports
getattr()/__getattr__/__getattribute__- function annotations (py3k feature, are ignored right now, but being parsed.
I don’t know what to do with them.) - class decorators (py3k feature, are being ignored too, until I find a use
case, that doesn’t work with Jedi) - simple/usual
sys.pathmodifications isinstancechecks for if/while/assert