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Theory predicts that, owing to reduced Hill-Robertson interference, genomic regions with high crossing-over rates should experience more efficient selection. In Saccharomyces cerevisiae a negative correlation between the local recombination rate, assayed as meiotic double-strand breaks (DSBs), and the local rate of protein evolution has been considered consistent with such a model. Although DSBs are a prerequisite for crossing-over, they need not result in crossing-over. With recent high-resolution crossover data, we now return to this issue comparing two species of yeast. Strikingly, even allowing for crossover rates, both the rate of premeiotic DSBs and of noncrossover recombination events predict a gene's rate of evolution. This both questions the validity of prior analyses and strongly suggests that any correlation between crossover rates and rates of protein evolution could be owing to slow-evolving genes being prone to DSBs or a direct effect of DSBs on sequence evolution. To ask if classical theory of recombination has any relevance, we determine whether crossover rates predict rates of protein evolution, controlling for noncrossover DSB events, gene ontology (GO) class, gene expression, protein abundance, nucleotide content, and dispensability. We find that genes with high crossing-over rates have low rates of protein evolution after such control, although any correlation is weaker than that previously reported considering meiotic DSBs as a proxy. The data are consistent both with recombination enhancing the efficiency of purifying selection and, independently, with DSBs being associated with low rates of evolution.