What can we learn from distributions of deaths by age cumulated over time such as those estimated from skeletons? Among the many solutions fitting the data (which are not necessarily stable populations but which satisfy the demographic equations with time-varying fertility and mortality), the solution with the minimum variations in the demographic forces provides a useful reference. This solution is generally not a stable population, and it can be achieved with a technique borrowed from simulated annealing optimization. This method, although complex, produces a more realistic reconstruction of the underlying population than previous methods. Simulations show that the mean life expectancy at birth, the mean total fertility rate, and the mean population size over the deposition period are accurately reconstructed although the fluctuations of the corresponding time series are not. Results are presented for case studies of the St. Thomas Anglican Church and Dallas Freedman's Cemeteries.