We present a new solution to partition function form games that is novel in at least two ways. Firstly, the solution exploits the consistency of the partition function form, namely that the response to a deviation is established as the same solution applied to the residual game, itself a partition function form game. This consistency allows us to model residual behaviour in a natural, intuitive way. Secondly, we consider a pair of solutions as the extrema of an interval for set inclusion. Taking the whole interval rather than just one of the extremes enables us to include or exclude outcomes with certainty.