Landings statistics can be lower than true catches because many fish are discarded or landed illegally. Since many discards do not survive, treating landings as true catches can lead to biased stock assessments. This paper proposes treating catch as censored by bounding it below by the landings, L, and above by cL (for scalar c > 1), We demonstrate the approach with a simulation study, using a Schaefer surplus production model. Parameters were estimated in a Bayesian framework with BUGS software using two sets of priors. Both the traditional true-catch method and a survey-and-effort method (which was landings free) performed worse on average than the censored approach, as measured by the Bayes risk associated with estimates of maximum sustainable yield (MSY) and of an index of depletion (X). Recursive partitioning (regression trees) was used to associate simulation parameters to best-performing methods, showing that higher commercial fish catchability favoured the censored method at estimating X. In conclusion, censored methods provide a means of dealing with discarding and misreporting that can outperform some traditional alternatives.