This paper has four purposes. First, we outline the controversy surrounding the issue of negative willingness to pay (WTP) in contingent valuation (CV) studies. Second, we use Monte Carlo simulation to examine the performance of alternative distributional assumptions in estimating WTP in the presence of varying proportions of the population holding negative WTP values. We focus on dichotomous choice CV (DC-CV), where negative WTP values may be especially difficult to detect. Third, we extend the simulation to investigate the performance of the mixture models that have recently been proposed for handling/identifying non-positive WTP values. Fourth, we extend the simulation to investigate the performance of the nonparametric lower bound Turnbull approach. Results indicate that the relative performance of the DC-CV modeling alternatives evaluated here, which assume positive WTP, varies across the simulation setting (e.g., proportion of negative WTP); but none can be said to reasonably ``solve'' the problem ex post. This underscores the importance of ex ante efforts to identify if negative WTP is likely to be prominent in a given valuation setting. In such cases, appropriately handling negative WTP must be addressed through ex ante survey design and modeling choices that allow negative WTP.