Systematic biases in reporting past behavior may compromise the methods used to derive values from revealed preference data. Recreational survey response data is routinely plagued by three problems: an abundance of zeros due to non-participation (the “excess-zero” problem), response “heaping”, and “leaping” of responses (issues resulting from recall bias). To simultaneously address these issues in the discrete data context, we consider several different specifications of the negative binomial estimator of recreation demand. We find that the negative binomial model’s fit is significantly improved by reassigning heaped responses to censored regimes where reported trip numbers form the intervals’ upper-bounds. To this end, we illustrate how employing the incomplete beta function to represent the cumulative distribution function of the negative binomial distribution simplifies the incorporation of censored intervals.