Diagnostic goodness-of-fit tests for capture–recapture models are routinely used prior to model fitting and analysis. However, when data include a mixture of live recaptures and dead recoveries, it is frequently standard practice for the information from recoveries not to be used, so that tests are applied to the recapture data alone. We present new diagnostic tests for joint recapture–recovery data, which make full use of all of the data, and evaluate their power through simulation. The importance of including all available data is clearly shown. We see in addition that current procedures may fail to identify the correct model. The work is generalised to the case of multi-site joint recapture–recovery data and is illustrated on a data set of great cormorants. This article has supplementary material online.