While data sets based on dense genome scans are becoming increasingly common, there are many theoretical questions that remain unanswered. How can a large number of markers in high linkage disequilibrium (LD) and rare disease variants be simulated efficiently? How should markers in high LD be analyzed: individually or jointly? Are there fast and simple methods to adjust for correlation of tests? What is the power penalty for conservative Bonferroni adjustments? Assuming that association scans are adequately powered, we attempt to answer these questions. Performance of single-point and multipoint tests, and their hybrids, is investigated using two simulation designs. The first simulation design uses theoretically derived LD patterns. The second design uses LD patterns based on real data. For the theoretical simulations we used polychoric correlation as a measure of LD to facilitate simulation of markers in LD and rare disease variants. Based on the simulation results of the two studies, we conclude that statistical tests assuming only additive genotype effects (i.e. Armitage and especially multipoint T(2)) should be used cautiously due to their suboptimal power in certain settings. A false discovery rate (FDR)-adjusted combination of tests for additive, dominant and recessive effects had close to optimal power. However, the common genotypic chi(2) test performed adequately and could be used in lieu of the FDR combination. While some hybrid methods yield (sometimes spectacularly) higher power they are computationally intensive. We also propose an "exact" method to adjust for multiple testing, which yields nominally higher power than the Bonferroni correction.