Unambiguous and Minimal Error discrimination are the two usual approaches to quantum state discrimination. In many practical instances however one may be interested in an approach between these two extremes. This is achieved by allowing certain rate of inconclusive answers. We present the optimal solution to this approach. We find the minimal discrimination error as a function of this inconclusive rate and find a critical rate that, in the cases where unambiguous discrimination is not possible, it yields what can be seen as the generalization of the optimal unambiguous discrimination.