Blanchard defined a topological dynamical system to have (topological) completely positive entropy (TCPE) if every nontrivial (i.e. not a single point) factor has positive entropy. We can define the related notion of zero-dimensional topological completely positive entropy (ZTCPE); a system has ZTCPE if every nontrivial zero-dimensional factor has positive entropy. It's trivial that these notions are not equivalent, but natural to wonder whether they are for systems which are themselves zero-dimensional. I'll discuss some positive and negative results related to this question and give some open questions.