In this article we consider three nonparametric maximum likelihood estimators based on mixed-case interval-censored data. Apart from the unrestricted estimator, we consider estimators under the assumption that the underlying distribution function of event times is concave or unimodal. Characterizations of the estimates are derived, and algorithms are proposed for their computation. The estimators are shown to be asymptotically consistent, and the benefits of additional constraints are illustrated through simulations. Finally, the estimators are used as an ingredient in a nonparametric comparison of two samples. © 2006 American Statistical Association.