Abstract The starting point of this talk is Bell’s procedure for developing classical logic by the use of the Epsilon Calculus on an intuitionistic basis. Bell’s argument will be analysed and some core building blocks used in order to obtain a similar, and, in fact, stronger, result. Resembling results are obtainable by using the original account of Hilbert & Bernays on Iota-terms. If time permits, we shall also have a look on multi-valued logics, and on how Epsilon- and Iota-terms behave in this environment.