Allele-specific sequencing reads provide a powerful signal for identifying molecular quantitative trait loci (QTLs), but they are challenging to analyze and are prone to technical artifacts. Here we describe WASP, a suite of tools for unbiased allele-specific read mapping and discovery of molecular QTLs. Using simulated reads, RNA-seq reads and chromatin immunoprecipitation sequencing (ChIP-seq) reads, we demonstrate that WASP has a low error rate and is far more powerful than existing QTL-mapping approaches.