We study the determination of gamma from CP-violating observables in B -> pi+ pi- and B -> psi K_S. This determination requires theoretical input to one combination of hadronic parameters. We show that a mild assumption about this quantity may allow bounds to be placed on gamma, but we stress the pernicious effects that an eightfold discrete ambiguity has on such an analysis. The bounds are discussed as a function of the direct (C) and interference (S) CP-violating observables obtained from time-dependent B -> pi+ pi- decays, and their behavior in the presence of new physics effects in B-Bbar mixing is studied. (V2: Misprints corrected. Slightly improved discussion.)
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