A priori voting power analysis can be useful in helping to design a weighted voting system that has certain intended properties. Power indices can help determine how many weighted votes each member should be allocated and what the decision rule should be. These choices can be made in the light of a requirement that there be a given distribution of power and/or a desired division of powers between individual members and the collective institution. This paper focuses on the former problem: choosing the weights given that the power indices and the decision rule are fixed exogenously.