Abstract Genome sequencing and genetic mapping of molecular markers has demonstrated Y-linkage across most of the guppy ( Poecilia reticulata ) XY chromosome pair. However, they also revealed exchanges with the X, consistent with classical genetic observations of occasional exchanges of factors controlling visible male-specific phenotypic traits. It remains unclear whether this fish species has an extensive sex-determining region without crossing over (whose suppressed recombination could have evolved under selection created by sexually antagonistic effects of male coloration factors), or whether the fully Y-linked region is very small, perhaps within a single gene. Population genomic data support cytogenetic results indicating that it is within the terminal 5 Mb of the 26.5 Mb chromosome 12, just proximal to a highly recombining pseudo-autosomal region, PAR1. Using molecular markers, we studied recombination, focusing on this region of the XY pair. Despite assembly errors in the small terminal PAR1, our mapping identifies very similar genetic PAR boundaries in sires from four populations, suggesting that their crossover patterns have not changed. Our results also confirmed occasional crossovers proximal to the male-determining region, defining a second pseudo-autosomal region, PAR2, recombining much more rarely than PAR1. The crossover positions suggest that the male-determining factor is within a repetitive region near 21 Mb in the female assembly. A sex-reversed XX male had few crossovers in PAR2, suggesting that this region’s low crossover rate depends on the phenotypic, not the genetic, sex. Thus rare sex changes, and/or occasional crossovers in males can explain the failure to detect fully Y-linked variants.