The adaptive value of recombination remains something of a puzzle. One of the basic problems is that recombination not only creates new and advantageous genetic combinations, but also breaks down existing good ones. A negative correlation between the fitness of an individual and its recombination rate would result in prolonged integrity of fitter genetic combinations while enabling less fit ones to produce new combinations. Such a correlation could be mediated by various factors, including stress responses, age, or direct DNA damage. For haploid population models, we show that an allele for such fitness-associated recombination (FAR) can spread both in asexual populations and in populations reproducing sexually at any uniform recombination rate. FAR also carries an advantage for the population as a whole, resulting in a higher average fitness at mutation-selection balance. These results are demonstrated in populations adapting to new environments as well as in well-adapted populations coping with deleterious mutations. Current experimental results providing evidence for the existence of FAR in nature are discussed.