Identifying genomic annotations that differentiate causal from trait-associated variants is essential to fine mapping disease loci. Although many studies have identified non-coding functional annotations that overlap disease-associated variants, these annotations often colocalize, complicating the ability to use these annotations for fine mapping causal variation. We developed a statistical approach (Genomic Annotation Shifter GoShifter) to assess whether enriched annotations are able to prioritize causal variation. GoShifter defines the null distribution of an annotation overlapping an allele by locally shifting annotations; this approach is less sensitive to biases arising from local genomic structure than commonly used enrichment methods that depend on SNP matching. Local shifting also allows GoShifter to identify independent causal effects from colocalizing annotations. Using GoShifter, we confirmed that variants in expression quantitative trail loci drive gene-expression changes though DNase-I hypersensitive sites (DHSs) near transcription start sites and independently through 3′ UTR regulation. We also showed that (1) 15%–36% of trait-associated loci map to DHSs independently of other annotations; (2) loci associated with breast cancer and rheumatoid arthritis harbor potentially causal variants near the summits of histone marks rather than full peak bodies; (3) variants associated with height are highly enriched in embryonic stem cell DHSs; and (4) we can effectively prioritize causal variation at specific loci.