Two heuristic algorithms are developed to handle combinatorial and discrete complications persistent in markets where total quantity is regulated. The algorithms account for trader heterogeneity, which could either be innate (as exists in a wide class of environmental problems) or imposed by the regulator to simultaneously achieve a social goal, such as distributional equity. In addition, the algorithms account for discreteness in the production technology of the tradable commodity. The cost efficiencies of the algorithms are demonstrated both through a simple example of pollution trading and by formal reasoning.