This paper considers optimization problems in which some or all variables must take on integral values. An ability to solve such problems would be valuable in itself, and would also allow us to handle certain kinds of heretofore intractable "economies of scale." We do not present an automatic algorithm for solving such problems. Rather we present a general approach susceptible to individual variations, depending upon the problem and the judgment of the user. Two moderate-size examples are presented to illustrate the method.