This study applies conjoint analysis to estimate health-related benefit-risk tradeoffs in a non-expected-utility framework. We demonstrate how this method can be used to test for and estimate nonlinear weighting of adverse-event probabilities and we explore the implications of nonlinear weighting on maximum acceptable risk (MAR) measures of risk tolerance. We obtained preference data from 570 Crohn's disease patients using a web-enabled conjoint survey. Respondents were presented with choice tasks involving treatment options that involve different efficacy benefits and different mortality risks for 3 possible side effects. Using conditional logit maximum likelihood estimation, we estimate preference parameters using 3 models that allow for nonlinear preference weighting of risks--a categorical model, a simple-weighting model, and a rank dependent utility (RDU) model. For the second 2 models we specify and jointly estimate 1- and 2-parameter probability weighting functions. Although the 2-parameter functions are more flexible, estimation of the 1-parameter functions generally performed better. Despite well-known conceptual limitations, the simple-weighting model allows us to estimate weighting function parameters that vary across 3 risk types, and we find some evidence of statistically significant differences across risks. The parameter estimates from RDU model with the single-parameter weighting function provide the most robust estimates of MAR. For an improvement in Crohn's symptom severity from moderate and mild, we estimate maximum 10-year mortality risk tolerances ranging from 2.6% to 7.1%. Our results provide further the evidence that quantitative benefit-risk analysis used to evaluate medical interventions should account explicitly for the nonlinear probability weighting of preferences.