True-amplitude migration of the Kirchhoff type is a task of high computational effort. A substantial part of this effort is spent on the calculation of proper weight functions to countermand the effect of geometrical spreading in the data. The generation of the weights is usually very time consuming. Also, the weights must be stored. Together with the traveltime tables which are needed for the stacking surfaces, this leads to large demands in computer storage in addition to the high requirements in CPU time. In this paper we propose a strategy to compute the weight functions directly from coarsely-gridded traveltimes. Together with a fast and accurate method for the interpolation of the traveltimes onto the required fine migration grid, this leads to considerable savings in CPU time as well as storage. Application to a complex synthetic data set demonstrates the high quality of our approach.