The properties of genotype-phenotype landscapes are crucial for understanding evolution but are not characterized for most traits. Here, we present a >95% complete local landscape for a defined molecular function-the alternative splicing of a human exon (FAS/CD95 exon 6, involved in the control of apoptosis). The landscape provides important mechanistic insights, revealing that regulatory information is dispersed throughout nearly every nucleotide in an exon, that the exon is more robust to the effects of mutations than its immediate neighbours in genotype space, and that high mutation sensitivity (evolvability) will drive the rapid divergence of alternative splicing between species unless it is constrained by selection. Moreover, the extensive epistasis in the landscape predicts that exonic regulatory sequences may diverge between species even when exon inclusion levels are functionally important and conserved by selection.