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We demonstrate that in the context of statically-typedpurely-functional lambda calculi without recursion, unchecked exceptions(e.g., SML exceptions) can be strictly more powerful than call/cc. Moreprecisely, we prove that a natural extension of the simply-typed lambdacalculus with unchecked exceptions is strictly more powerful than allknown sound extensions of Girard‘s F_ω (a superset of thesimply-typed lambda calculus) with call/cc.This result is established by showing that the first language is Turingcomplete while the later languages permit only a subset of the recursivefunctions to be written. We show that our natural extension of thesimply-typed lambda calculus with unchecked exceptions is Turingcomplete by reducing the untyped lambda calculus to it by means of anovel method for simulating recursive types usingunchecked-exception–returning functions. The result concerningextensions of F_ω with call/cc stems from previous work of theauthor and Robert Harper.