We improve the quality of cryptographically privacy-preserving genome-wide association studies by correctly handling population stratification-the inherent genetic difference of patient groups, e.g., people with different ancestries. Our approach is to use principal component analysis to reduce the dimensionality of the problem so that we get less spurious correlations between traits of interest and certain positions in the genome. While this approach is commonplace in practical genomic analysis, it has not been used within a privacy-preserving setting. In this paper, we use cryptographically secure multi-party computation to tackle principal component analysis, and present an implementation and experimental results showing the performance of the approach.