Studies on population history are often based on incomplete records of life histories. For instance, in studies using data obtained from family reconstitution, the date of death is right censored (by migration) and the censoring time is never observed. Several methods for the correction of mortality estimates are proposed in the literature, most of which first estimate the number of individuals at risk and then use standard techniques to estimate mortality. Other methods are based on statistical models. In this paper all methods are reviewed, and their merits are compared by applying them to simulated and to seventeenth-century data from the English parish of Reigate. An ad hoc method proposed by Ruggles performs reasonably well. Methods based on statistical models, provided they are sufficiently realistic, give comparable accuracy and allow the estimation of several other quantities of interest, such as the distribution of migration times.