A multilevel logistic model for estimating a nonlinear trajectory in a multiple-baseline design is introduced. The model is applied to data from a real multiple-baseline design study to demonstrate interpretation of relevant parameters. A simple change-in-levels (?"Levels") model and a model involving a quadratic function ("Quadratic") for the nonlinear intervention phase data were also estimated. In addition, a simulation study was conducted to assess Markov chain Monte Carlo estimation of the logistic model and compare its trajectory recovery with use of the ?"Levels" and "Quadratic" models. While most of the logistic model's parameter values were recovered well, trajectory recovery was very reasonable using the simpler "Quadratic" model. Results are discussed along with recommendations for practitioners and directions for future research.