The effects of human-caused mortality, such as fisheries bycatch, of endangered, threatened and protected (ETP) species of marine mammals can be evaluated using population model-based stock assessments. The information available to conduct such assessments is often very limited. Available data might include fragmented time-series of abundance estimates, incomplete data on bycatch for the fisheries that interact with ETP species (often few years and low observer coverage), and perhaps some data on scale and trends in fishing effort. Such data are challenging to use as the basis for stock assessments, which generally assume that estimates of removals (bycatch, in our context) through time are available for at least the most recent decade or two. This paper describes a stock assessment method for use with sparse observer data on bycatch mortality, applied within the context of a Bayesian estimation framework. The method produces estimates, with associated measures of precision, of population size and historical time-series of bycatch mortality that are consistent with the observer and abundance data. It provides a rigorous way to account for the uncertainty arising from animals that are caught but released alive and then die subsequent to release, given a post-release mortality rate prior. Observer data from industrial and artisanal purse seine and trawl fisheries and survey data for South American sea lions (Otaria byronia) and South American fur seals (Arctocephalus australis) off Chile are used to illustrate the method.