Non-parametric linkage analysis methods generally involve calculating an allele-sharing statistic for each pedigree in a data set, then standardizing and summing the statistics over pedigrees. Pedigrees of different sizes can be weighted differently in the sum, though it is perhaps most common to weight all standardized pedigree statistics equally. Most other common weighting schemes are based on the number of affected individuals in the pedigree. It is also possible to derive optimal weights, which maximize power to detect linkage under particular trait models. We started by investigating three different analytical and simulation-based methods to calculate power and derive optimal weights. We found that simulation methods produce noticeably more accurate power calculations than the other methods. However, although the different calculation methods give different "optimal" weights, the power at those weights is very similar. That is, the analytical calculation methods are sufficient for finding good weights even though the simulation methods are most appropriate for calculating power. In comparing optimal weights for different trait models, we found that the weights vary quite a bit with the model, such that optimal weights for one model are not necessarily powerful at all for other models. Finally, we studied the power of a number of general weighting schemes, and of some new ones that incorporate information on how closely the affected individuals are related. We were able to find some schemes that performed well in the sense of giving reasonably powerful weights for most of the trait models and pedigree types we considered.