Demographic estimates for small areas within a country have many uses. Subnational population estimation is, however, difficult, requiring the synthesis of multiple inconsistent datasets. Current methods have important limitations, including a heavy reliance on ad hoc adjustment and limited allowance for uncertainty. In this paper we demonstrate how subnational population estimation can be carried out within a formal Bayesian framework. The core of the framework is a demographic account, providing a complete description of the demographic system. Regularities within the demographic account are described by a system model. The relationship between the demographic account and the observable data is described by an observation model. Posterior simulation is carried out using Markov chain Monte Carlo methods. We illustrate the methods using data for six regions within New Zealand.