What advantage might sexual recombination confer? Population genetics theory predicts that asexual genomes are less efficient at eliminating deleterious mutations and incorporating beneficial alleles. Here, I compare patterns of genome evolution in a 40-kb gene-rich region on homologous neo-sex chromosomes of Drosophila miranda. Genes on the non-recombining neo-Y show various signs of degeneration, including transposable-element insertions, frameshift mutations and a higher rate of amino-acid substitution. In contrast, loci on the recombining neo-X show intact open reading frames and generally low rates of amino-acid substitution. One exceptional gene on the neo-X shows evidence for adaptive protein evolution, affecting patterns of variability at neighboring regions along the chromosome. These findings illustrate the limits to natural selection in an asexual genome. Deleterious mutations, including repetitive DNA, accumulate on a non-recombining chromosome, whereas rapid protein evolution due to positive selection is confined to the recombining homolog.