The contribution of regulatory versus protein change to adaptive evolution has long been controversial. In principle, the rate and strength of adaptation within functional genetic elements can be quantified on the basis of an excess of nucleotide substitutions between species compared to the neutral expectation or from effects of recent substitutions on nucleotide diversity at linked sites. Here, we infer the nature of selective forces acting in proteins, their UTRs and conserved noncoding elements (CNEs) using genome-wide patterns of diversity in wild house mice and divergence to related species. By applying an extension of the McDonald-Kreitman test, we infer that adaptive substitutions are widespread in protein-coding genes, UTRs and CNEs, and we estimate that there are at least four times as many adaptive substitutions in CNEs and UTRs as in proteins. We observe pronounced reductions in mean diversity around nonsynonymous sites (whether or not they have experienced a recent substitution). This can be explained by selection on multiple, linked CNEs and exons. We also observe substantial dips in mean diversity (after controlling for divergence) around protein-coding exons and CNEs, which can also be explained by the combined effects of many linked exons and CNEs. A model of background selection (BGS) can adequately explain the reduction in mean diversity observed around CNEs. However, BGS fails to explain the wide reductions in mean diversity surrounding exons (encompassing ~100 Kb, on average), implying that there is a substantial role for adaptation within exons or closely linked sites. The wide dips in diversity around exons, which are hard to explain by BGS, suggest that the fitness effects of adaptive amino acid substitutions could be substantially larger than substitutions in CNEs. We conclude that although there appear to be many more adaptive noncoding changes, substitutions in proteins may dominate phenotypic evolution.