We prove that AM (and hence Graph Nonisomorphism) is in NP if for some > 0, some language in NE \ coNE requires nondeterministic circuits of size 2 n . This improves recent results of Arvind and K obler and of Klivans and Van Melkebeek who proved the same conclusion, but under stronger hardness assumptions, namely, either the existence of a language in NE \ coNE which cannot be approximated by nondeterministic circuits of size less than 2 n or the existence of a language in NE \ coNE which requires oracle circuits of size 2 n with oracle gates for SAT (satisfiability). The previous results on derandomizing AM were based on pseudorandom generators. In contrast, our approach is based on a strengthening of Andreev, Clementi and Rolim's hitting set approach to derandomization. As a spin-off, we show that this approach is strong enough to give an easy (if the existence of explicit dispersers can be assumed known) proof of the following implication: For some > 0, if there is a l..