Many countries, particularly in the developing world, have inadequate vital registration systems, and data collected by population censuses in these countries often contain serious and predictable biases. Direct methods of measuring mortality are useless in such situations, so indirect methods have been developed instead. The two best known indirect methods, namely estimating childhood mortality from the proportion dead among children ever borne by women of known age, and estimating adult mortality from reports of orphanhood by age, are discussed. Various shortcomings of the orphanhood method are noted, particularly in its application to estimating adult male mortality. To avoid these, two different approaches are suggested, developed and tested. One is to limit the analysis of orphanhood to reports of the eldest surviving child of each parent only, and the other is to analyse proportions widowed of first spouse. It is not difficult to develop a method of analysis for estimating mortality from reports of firstborn children, but using reports of eldest surviving children is more complicated. Allowance has to be made for deaths among firstborn children, and their replacement by second or higher order children. A simple model was developed to work out the birth order composition of eldest surviving children at various ages. The method of analysis so developed has certain advantages over the original orphanhood method, but is found to be very sensitive to changes in the level and age pattern of mortality. The method of analysis developed for widowhood data is much simpler. The only complication is the need for two marriage distributions, male and female, the one to calculate the probability of being widowed for a given exposure to risk, and the other to work out the exposure to risk of a particular age group of respondents. The method proves to be robust to changes in mortality and to deviations from the other crucial assumptions on which it is based. Both methods are applied to suitable data collected by a sample survey in Honduras. The data and the results are critically examined to assess both the possibility of collecting the required data and the success of the methods themselves. The conclusion is drawn that the widowhood method is promising, but the orphanhood of eldest surviving children method is disappointing. More applications are needed, though, to establish whether either or both of these methods are worthy of a place amongst the standard techniques for estimating population parameters in countries having defective or incomplete data.