A challenge for integrated population methods is to examine the extent to which different surveys that measure different demographic features for a given species are compatible. Do the different pieces of the jigsaw fit together? One convenient way of proceeding is to generate a likelihood for census data using the Kalman filter, which is then suitably combined with other likelihoods that might arise from independent studies of mortality, fecundity, and so forth. The combined likelihood may then be used for inference. Typically the underlying model for the census data is a state-space model, and capture–recapture methods of various kinds are used to construct the additional likelihoods. In this paper we provide a brief review of the approach; we present a new way to start the Kalman filter, designed specifically for ecological processes; we investigate the effect of break-down of the independence assumption; we show how the Kalman filter may be used to incorporate density-dependence, and we consider the effect of introducing heterogeneity in the state-space model.