This text addresses one of the major inverse problems in population ecology - that of inferring mortality rates from population numbers for a set of age classes or developmental stages. The authors set out to provide a useful method for field ecologists, and a framework from which to approach future problems. After a survey of previously published methods, an analysis is given of some basic instabilities that arise in the process of mortality estimation from stage structured population data. A concise introduction to spline theory, and the derivation of some new results, enables these instabilities to be overcome in a biologically sensible way. The resulting methods are then tested on simulated data, and their performance compared with that of previous methods. Finally, a real system with three species is investigated using the new methods.