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This paper studies the power of three types of access to unambiguous computation: nonadaptive access, fault-tolerant access, and guarded access. (1) Though for NP it is known that nonadaptive access has exponentially terse adaptive simulations, we show that UP has no such relativizable simulations: there are worlds in which (k+1)-truth-table access to UP is not subsumed by k-Turing access to UP. (2)...