Multibeam satellite systems have the potential to substantially increase the capacity of the wholesystem. In this paper, we study the criteria in multibeamsatellite downlinks weighting vector design and propose anew tradeoff power allocation algorithm. Traditional algorithms, such as maximum capacity and proportional fairness, can not make a compromise between total capacitymaximization and uses' fairness. The new algorithm, whichwe call `tradeoff allocation', is based on maximum capacityalgorithm, and simply changes its cost function to provide asensible compromise between total capacity maximizationand fairness. Compared with other compromise algorithm,tradeoff allocation algorithm is simpler and more flexible,because the different choose of parameter can provide different allocation. In addition, we also propose priority allocation strategy and it can optimize traditional allocationalgorithm and make the power allocation more reasonablein special practical application.