Trakhtenbrot calls a setA autoreducible ifA is Turing-reducible toA via an oracle Turing machine that never queries the oracle about the input string. Yao considers sets that are autoreducible via probabilistic, polynomial-time oracle Turing machines, and he calls such setscoherent. We continue the study of autoreducible sets, including those that are autoreducible via a family of polynomial-sized circuits, which we callweakly coherent. Sets that are not weakly coherent are calledstrongly incoherent. We show Ifs is superpolynomial and space-constructible, then there is a strongly incoherent set in DSPACE (s(n)). If NEEEXP\( \nsubseteq \) BPEEEXP, then there is a set in NP that is incoherent. IfA is complete for any of the classes ∑ i p , ∏ i p , or Δ i p ,i≥0, thenA is coherent. In particular, all NP-complete sets are coherent.