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I've got a big expression I need to dissect a certain way

I've got a BIG polynomial (7 indeterminates, total degree 12), and I want to collect all the terms therein that contain only EVEN powers of all the indeterminates. Is there any reasonably simple way to do this? By "simple," I mean short of traversing the whole expression tree, testing each term to see if it contains only even powers, and collecting them one-by-one in a list (which, BTW, I also don't really know how to do)! If it makes any difference, I haven't been using the sage.rings.polynomial module, just generic Sage expressions.