1. Mark-recapture models are valuable for assessing diverse demographic and behavioural parameters, yet the precision of traditional estimates is often constrained by sparse empirical data. Bayesian inference explicitly recognizes estimation uncertainty, and hierarchical Bayes has proven particularly useful for dealing with sparseness by combining information across data sets. 2. We developed a general hierarchical Bayesian multi-state mark-recapture model, tested its performance on simulated data sets and applied it to real ecological data on stopovers by migratory birds. 3. Our hierarchical model performed well in terms of both precision and accuracy of parameters when tested with simulated data of varying quality (sample size, capture and survivorship probabilities). It also provided more precise and accurate parameter estimates than a non-hierarchical model when data were sparse. 4. A specific version of the model, designed for estimation of daily transience and departure of migratory birds at a mid-route stopover, was applied to 11 years of autumn migration data from Atlantic Canada. Hierarchical estimates of departure and transience were more precise than those derived from parallel non-hierarchical and frequentist methods, and indicated that inter-annual variability in parameters suggested by these other methods was largely due to sampling error. 5. Synthesis and applications. Estimates of demographic parameters, often derived from mark-recapture studies, provide the basis for evaluating the status of species at risk, for developing conservation and management strategies and for evaluating the results of current protocols. The hierarchical Bayesian multi-state mark-recapture model presented here permits partitioning of complex parameter variation across space or time, and the simultaneous analysis of multiple data sets results in a marked increase in the precision of estimates derived from sparse capture data. Its structural flexibility should make it a valuable tool for conservation ecologists and wildlife managers.