Doubly truncated data are often encountered in the analysis of survival times, when the sample reduces to those individuals with terminating event falling on a given observational window. In this paper we assume that some information about the bivariate distribution function (df) of the truncation times is available. More specifically, we represent this information by means of a parametric model for the joint df of the truncation times. Under this assumption, a new semiparametric estimator of the lifetime df is derived. We obtain asymptotic results for the new estimator, and we show in simulations that it may be more efficient than the Efron–Petrosian nonparametric maximum likelihood estimator. Data on the age at diagnosis of childhood cancer in North Portugal are analyzed with the new method.