Controlling for background demographic effects is important for accurately identifying loci that have recently undergone positive selection. To date, the effects of demography have not yet been explicitly considered when identifying loci under selection during dog domestication. To investigate positive selection on the dog lineage early in the domestication, we examined patterns of polymorphism in six canid genomes that were previously used to infer a demographic model of dog domestication. Using an inferred demographic model, we computed false discovery rates (FDR) and identified 349 outlier regions consistent with positive selection at a low FDR. The signals in the top 100 regions were frequently centered on candidate genes related to brain function and behavior, including LHFPL3, CADM2, GRIK3, SH3GL2, MBP, PDE7B, NTAN1, and GLRA1. These regions contained significant enrichments in behavioral ontology categories. The 3rd top hit, CCRN4L, plays a major role in lipid metabolism, that is supported by additional metabolism related candidates revealed in our scan, including SCP2D1 and PDXC1. Comparing our method to an empirical outlier approach that does not directly account for demography, we found only modest overlaps between the two methods, with 60% of empirical outliers having no overlap with our demography-based outlier detection approach. Demography-aware approaches have lower-rates of false discovery. Our top candidates for selection, in addition to expanding the set of neurobehavioral candidate genes, include genes related to lipid metabolism, suggesting a dietary target of selection that was important during the period when proto-dogs hunted and fed alongside hunter-gatherers.