Recently, a new family of power indices, the FP, was introduced by Fragnelli, Ottone and Sattanino (2009), requiring that the parties of a majority are ideologically contiguous along a left-right axis. The different choices of some parameters allow representing various situations, resulting in different indices in this family. In this paper we analyze how to select the parameters with the aim of transferring some properties of classical power indices. We start by relaxing the hypothesis of contiguity. Then, we reduce the relevance of non-contiguous coalitions, defining a sequence of indices that converges to a modified version of the classical indices. The method is applied to the Italian lower chamber. Finally, we extend our approach to situations in which the parties are not necessarily ordered according to the left-right axis, expressing their relations by a graph, following the idea of Myerson (1977).