Integrated population modelling is widely used in ecology when data at the individual level are combined with independent time series measuring population abundance. However there is no formal assessment of how to select the best integrated model. Here we focus on the important case of determining the age-structure for annual survival probabilities of wild animals, involving comparing state–space models with different numbers of states. The work is motivated by real data sets, and evaluated by simulation. We reject the naïve use of AIC, and advocate the use of likelihood-ratio tests, based on combined data. We demonstrate using simulation that typical asymptotic chi-square distributions of likelihood-ratio test statistics to compare integrated models apply when the corresponding state–space models have the same state variables. In addition, for linear state–space models with matching initial conditions the correct chi-square distributions may also hold when models apparently have different state–spaces. The results for comparing integrated models also have relevance for state–space modelling alone. A senescence case study is provided which incorporates a step-up approach and illustrates the use of the recommendations of the paper in practice.