What is a clean, Pythonic way to have multiple constructors in Python?

Actually None is much better for “magic” values:

class Cheese():
    def __init__(self, num_holes = None):
        if num_holes is None:
            ...

Now if you want complete freedom of adding more parameters:

class Cheese():
    def __init__(self, *args, **kwargs):
        #args -- tuple of anonymous arguments
        #kwargs -- dictionary of named arguments
        self.num_holes = kwargs.get('num_holes',random_holes())

To better explain the concept of *args and **kwargs (you can actually change these names):

def f(*args, **kwargs):
   print 'args: ', args, ' kwargs: ', kwargs

>>> f('a')
args:  ('a',)  kwargs:  {}
>>> f(ar='a')
args:  ()  kwargs:  {'ar': 'a'}
>>> f(1,2,param=3)
args:  (1, 2)  kwargs:  {'param': 3}

http://docs.python.org/reference/expressions.html#calls