I think you're looking for the more powerful "Combobox" in ttk (also in standard python as simple extensions to Tk).
As effbot puts it
The option menu is similar to the combobox
For example:
from tkinter.ttk import Combobox # python 3 notation
combo = Combobox(root,values=['a','aa','aaaaa','aaaaaaa'],width=3)
It will simply cut off the elements that are too long
(If you're in python 2 it's slightly different to import ttk)
If you want a nice "..." to appear when cutting off entries, I think you're best bet is to
elements = ['a','aa','aaaaaaaa']
simple_values = [ e[:3] + ('...' if len(e) > 3 else '') for e in elements]
combo = Combobox(root,values=simple_values )
If you need to be able to map between them, use your favorite data structure or reference by index not value in the combobox