We present a new strategy for RANSAC sampling named BetaSAC, in reference to the beta distribution. Our proposed sampler builds a hypothesis set incrementally, select- ing data points conditional on the previous data selected for the set. Such a sampling is shown to provide more suitable samples in terms of inlier ratio but also of consistency and potential to lead to an accurate parameters estimation. The algorithm is presented as a general framework, easily implemented and able to exploit any kind of prior infor- mation on the potential of a sample. As with PROSAC, BetaSAC converges towards RANSAC in the worst case. The benefits of the method are demonstrated on the homog- raphy estimation problem.