This paper answers three questions related to the discrete nature of pollution abatement: (i) does a source's incremental control cost necessarily exceed its average control cost, (ii) is incremental control cost a better approximation of a source's willingness to pay for abatement credits than average control cost, and (iii) exactly how do discrete and continuous abatement markets differ from one another? We find that the answer to the first two questions are both "no," suggesting that the U.S. Environmental Protection Agency needs to refine its reliance on incremental control cost as the sole measure upon which to assess the financial feasibility of water quality trading. In answer to the third question, the equilibrium outcome for a discrete abatement market can be solved through a process of implicit sequential consistency. For the general case where the sources' average control cost curves "cross," the equilibrium is inherently sensitive to the initial allocation of abatement responsibilities.