Gene duplications allow evolution of genes with new functions. Here, we describe the innovation-amplification-divergence (IAD) model in which the new function appears before duplication and functionally distinct new genes evolve under continuous selection. One example fitting this model is a preexisting parental gene in Salmonella enterica that has low levels of two distinct activities. This gene is amplified to a high copy number, and the amplified gene copies accumulate mutations that provide enzymatic specialization of different copies and faster growth. Selection maintains the initial amplification and beneficial mutant alleles but is relaxed for other less improved gene copies, allowing their loss. This rapid process, completed in fewer than 3000 generations, shows the efficacy of the IAD model and allows the study of gene evolution in real time.