In many cancer registries, registration of new cases is somewhat less up-to-date than mortality follow-up. In such situations, hybrid analysis, a combination of cohort and period analysis, rather than 'pure' period analysis has been proposed to derive up-to-date survival estimates. We evaluate application and adaptation of a modelling strategy that has recently been introduced to enhance precision of period survival estimates, to 'hybrid type of data'. Using data from the Finnish Cancer Registry, we show that modelling again strongly increases precision of survival estimates. Furthermore, special models adapted to the hybrid type of data are shown to provide even more precise and, in a clear majority of cases, also more valid predictions of survival of recently diagnosed patients than models ignoring the hybrid type of data. Finally, we show that model-based estimation of and testing for recent trends may give different answers if period rather than hybrid modelling is used for hybrid type of registry data. We conclude that modelling is useful for both hybrid and period analyses of cancer survival, but the different data structure needs to be taken into account in the set-up of models.