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Complete knowledge of the genetic variation in individual human genomes is a crucial foundation for understanding the etiology of disease. Genetic variation is typically characterized by sequencing individual genomes and comparing reads to a reference. Existing methods do an excellent job of detecting variants in approximately 90% of the human genome; however, calling variants in the remaining 10% of the genome (largely low-complexity sequence and segmental duplications) is challenging. To improve variant calling, we developed a new algorithm, DISCOVAR, and examined its performance on improved, low-cost sequence data. Using a newly created reference set of variants from the finished sequence of 103 randomly chosen fosmids, we find that some standard variant call sets miss up to 25% of variants. We show that the combination of new methods and improved data increases sensitivity by several fold, with the greatest impact in challenging regions of the human genome.