The SRY gene on the mammalian Y chromosome undoubtedly acts to determine testis, but it is still quite unclear how. It was originally supposed that SRY acts directly to activate other genes in the testis-determining pathway. This paper presents an alternative hypothesis that SRY functions indirectly, by interacting with related genes SOX3 (from which SRY evolved) and SOX9 (which appears to be intimately involved in vertebrate gonad differentiation). Specifically, I propose that in females SOX3 inhibits SOX9 function, but in males, SRY inhibits SOX3 and permits SOX9 to enact its testis-determining role. This hypothesis makes testable predictions of the phenotypes of XX and XY individuals with deficiencies or overproduction of any of the three genes, and is able to account for the difficult cases of XX(SRY-) males and transdifferentiation in the absence of SRY. The hypothesis also suggests a way that the dominant SRY sex-determining system of present-day mammals may have evolved from an ancient system relying on SOX3 dosage.