In almost all existing semantics in argumentation, a strong attack has a lethal effect on its target that a set of several weak attacks may not have. This paper investigates the case where several weak attacks may compensate one strong attack. It defines a broad class of ranking semantics, called alpha-BBS, which satisfy compensation. alpha-BBS assign a burden number to each argument and order the arguments with respect to those numbers. We study formal properties of alpha-BBS, implement an algorithm that calculates the ranking, and perform experiments that show that the approach computes the ranking very quickly. Moreover, an approximation of the ranking can be provided at any time.