GWAS have emerged as popular tools for identifying genetic variants that are associated with disease risk. Standard analysis of a case-control GWAS involves assessing the association between each individual genotyped SNP and disease risk. However, this approach suffers from limited reproducibility and difficulties in detecting multi-SNP and epistatic effects. As an alternative analytical strategy, we propose grouping SNPs together into SNP sets on the basis of proximity to genomic features such as genes or haplotype blocks, then testing the joint effect of each SNP set. Testing of each SNP set proceeds via the logistic kernel-machine-based test, which is based on a statistical framework that allows for flexible modeling of epistatic and nonlinear SNP effects. This flexibility and the ability to naturally adjust for covariate effects are important features of our test that make it appealing in comparison to individual SNP tests and existing multimarker tests. Using simulated data based on the International HapMap Project, we show that SNP-set testing can have improved power over standard individual-SNP analysis under a wide range of settings. In particular, we find that our approach has higher power than individual-SNP analysis when the median correlation between the disease-susceptibility variant and the genotyped SNPs is moderate to high. When the correlation is low, both individual-SNP analysis and the SNP-set analysis tend to have low power. We apply SNP-set analysis to analyze the Cancer Genetic Markers of Susceptibility (CGEMS) breast cancer GWAS discovery-phase data.