In most sexual, diploid eukaryotes, at least one crossover occurs between each pair of homologous chromosomes during meiosis, presumably in order to ensure proper segregation. Well-known exceptions to this rule are species in which one sex does not recombine and specific chromosomes lacking crossover. We review other possible exceptions, including species with chromosome maps of less than 50 cM in one or both sexes. We discuss the idea that low recombination rates may favour sex-asex transitions, or, alternatively may be a consequence of it. We then show that a yet undescribed species of brine shrimp from Kazakhstan ( sp. Kazakhstan), the closest known relative of the asexual , has one of the shortest genetic linkage maps known. Based on a family of 42 individuals and 589 RAD markers, we find that many linkage groups are considerably shorter than 50 cM, suggesting either no obligate crossover or crossovers concentrated at terminal positions with little effect on recombination. We contrast these findings with the published map of the more distantly related sexual congener,, and conclude that the study of recombination in non-model systems is important to understand the evolutionary causes and consequences of recombination.This article is part of the themed issue 'Evolutionary causes and consequences of recombination rate variation in sexual organisms'.