A choice function C on X identifies, for each subset Y of X, a set C(Y) of "best" alternatives in Y. A. computationally viable choice function is one for which a member of the choice set C(Y) can be located by a computational procedure which does not waste time, generates reasonably satisfactory intermediate alternatives, and adjusts easily as new alternatives become available. Computational viability is defined precisely and the class of computationally viable choice functions is neatly characterized. In addition, the various types of binary choice functions are distinguished in terms of computational criteria.