This paper answers three questions related to the discrete nature of pollution abatement: (i) does a source's incremental control cost (as defined by the U.S. Environmental Protection Agency) 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 does trading in discrete and continuous abatement markets differ? 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, we show that the outcome of bilateral trading in the presence of discrete abatement is determined by comparing the gains from trade associated with the full sequence of possible “sunk cost trading” scenarios. For the most common case where trading partners' average control cost curves "cross," the trading outcome with discrete abatement is inherently sensitive to the initial allocation of abatement responsibilities.