SEX involves syngamy (gamete fusion), which doubles the amount of DNA in a cell, and meiosis(1), which halves it. The result is a ’ploidy cycle’ of alternating diploid and haploid phases. Asexual reproduction does not require changes of ploidy, and yet asexual forms may have ploidy cycles. Here I show that such cycles lessen the mutation load, compared with permanent diploidy or polyploidy, and are thus likely to evolve in cases where it is always advantageous to have more than one copy of the genome per cell. The asexual ploidy cycle could have facilitated the origin of sex, by providing a means of orderly genetic reduction available immediately after the origin of syngamy.