An important goal of evolutionary biology is to understand the constraints that shape the dynamics and outcomes of evolution. Here, we address the extent to which the structure of the standard genetic code constrains evolution by analyzing adaptive mutations of the antibiotic resistance gene TEM-1 β-lactamase and the fitness distribution of codon substitutions in two influenza hemagglutinin inhibitor genes. We find that the architecture of the genetic code significantly constrains the adaptive exploration of sequence space. However, the constraints endow the code with two advantages: the ability to restrict access to amino acid mutations with a strong negative effect and, most remarkably, the ability to enrich for adaptive mutations. Our findings support the hypothesis that the standard genetic code was shaped by selective pressure to minimize the deleterious effects of mutation yet facilitate the evolution of proteins through imposing an adaptive mutation bias.