By using a bit-string model of evolution, we find a successful route to dip
loidy and sex in simple organisms. Allowing the sexually reproducing diploi
d individuals to also perform mitosis, as they do in a haploid-diploid cycl
e, leads to the complete takeover of the population by sexual diploids. Thi
s mechanism is so robust that even the accidental conversion and pairing of
only two diploids give rise to a sexual population.