Understanding the process of adaptation during rapid environmental change remains one of the central focal points of evolutionary biology. The recently formed White Sands system of southern New Mexico offers an outstanding example of rapid adaptation, with a variety of species having rapidly evolved blanched forms on the dunes that contrast with their close relatives in the surrounding dark soil habitat. In this study, we focus on two of the White Sands lizard species, Sceloporus cowlesi and Aspidoscelis inornata, for which previous research has linked mutations in the melanocortin-1 receptor gene (Mc1r) to blanched coloration. We sampled populations both on and off the dunes and used a custom sequence capture assay based on probed fosmid libraries to obtain >50 kb of sequence around Mc1r and hundreds of other random genomic locations. We then used model-based statistical inference methods to describe the demographic and adaptive history characterizing the colonization of White Sands. We identified a number of similarities between the two focal species, including strong evidence of selection in the blanched populations in the Mc1r region. We also found important differences between the species, suggesting different colonization times, different genetic architecture underlying the blanched phenotype and different ages of the beneficial alleles. Finally, the beneficial allele is dominant in S. cowlesi and recessive in A. inornata, allowing for a rare empirical test of theoretically expected patterns of selective sweeps under these differing models.