We use a coupled map lattice to investigate the dynamics of a system of populations linked by dispersal, when dispersal incurs an additional mortality cost. Considering a single isolated population first, we show analytically that imposing an additional mortality term can stabilise the non-trivial steady state only under certain conditions. We demonstrate algebraically that in the absence of mortality during dispersal, linking a number of similar populations does not affect whether or not the equilibrium will be stable, although it can affect the nature of any unstable dynamics. Adding a fixed mortality rate during dispersal has a strong stabilising effect on system dynamics. We show analytically that for any combination of intrinsic reproduction parameters, a range of dispersal rates and dispersal mortalities can be found which together act to stabilise the equilibrium. Our results are shown numerically to be robust against a number of perturbations. Hence dispersal mortality has a strong stabilising effect on dynamics. In natural systems, some losses during long-distance dispersal are likely, and so we suggest that this factor could be an important determinant of the strength of observed population fluctuations. Copyright 1997 Academic Press Limited