Identifying adaptively important loci in recently bottlenecked populations - be it natural selection acting on a population following the colonization of novel habitats in the wild, or artificial selection during the domestication of a breed - remains a major challenge. Here we report the results of a simulation study examining the performance of available population-genetic tools for identifying genomic regions under selection. To illustrate our findings, we examined the interplay between selection and demography in two species of Peromyscus mice, for which we have independent evidence of selection acting on phenotype as well as functional evidence identifying the underlying genotype. With this unusual information, we tested whether population-genetic-based approaches could have been utilized to identify the adaptive locus. Contrary to published claims, we conclude that the use of the background site frequency spectrum as a null model is largely ineffective in bottlenecked populations. Results are quantified both for site frequency spectrum and linkage disequilibrium-based predictions, and are found to hold true across a large parameter space that encompasses many species and populations currently under study. These results suggest that the genomic footprint left by selection on both new and standing variation in strongly bottlenecked populations will be difficult, if not impossible, to find using current approaches.