In genetic association studies, much effort has focused on moving beyond the initial single-nucleotide polymorphism (SNP)-by-SNP analysis. One approach is to reanalyze a chromosomal region where an association has been detected, jointly analyzing the SNP thought to best represent that association with each additional SNP in the region. Such joint analyses may help identify additional, statistically independent association signals. However, it is possible for a single genetic effect to produce joint SNP results that would typically be interpreted as two distinct effects (e.g., both SNPs are significant in the joint model). We present a general approach that can (1) identify conditions under which a single variant could produce a given joint SNP result, and (2) use these conditions to identify variants from a list of known SNPs (e.g., 1000 Genomes) as candidates that could produce the observed signal. We apply this method to our previously reported joint result for smoking involving rs16969968 and rs588765 in CHRNA5. We demonstrate that it is theoretically possible for a joint SNP result suggestive of two independent signals to be produced by a single causal variant. Furthermore, this variant need not be highly correlated with the two tested SNPs or have a large odds ratio. Our method aids in interpretation of joint SNP results by identifying new candidate variants for biological causation that would be missed by traditional approaches. Also, it can connect association findings that may seem disparate due to lack of high correlations among the associated SNPs.