The paper establishes that every introenumerable set contains a uniformly introreducible subset, but it leaves open whether this subset can always be chosen to itself be introenumerable. Introenumerable sets are those that can be enumerated using themselves as an oracle in a uniform way, and uniform introreducibility is a stronger internal coherence condition on how the set relates to its own computation. The question is whether these two structural properties, both concerning a set's relationship to its own algorithmic content, can always be simultaneously satisfied within a single subset.