Comparisons between haplotypes from affected patients and the human reference genome are frequently used to identify candidates for disease-causing mutations, even though these alignments are expected to reveal a high level of background neutral polymorphism. This limits the scope of genetic studies to relatively small genomic intervals, because current methods for distinguishing potential causal mutations from neutral variation are inefficient. Here we describe a new strategy for detecting mutations that is based on comparing affected haplotypes with closely matched control sequences from healthy individuals, rather than with the human reference genome. We use theory, simulation, and a real data set to show that this approach is expected to reduce the number of sequence variants that must be subjected to follow-up analysis by at least a factor of 20 when closely matched control sequences are selected from a reference panel with as few as 100 control genomes. We also define a reference data resource that would allow efficient application of this strategy to large critical intervals across the genome.