Fully asexual lineages cannot purge accumulating mutations from their genome through recombination. In ancient asexuals that have persisted without sex for millions of years, this should lead to high allelic divergences (the 'Meselson effect') as has been shown for bdelloid rotifers. Homogenizing mechanisms can counter this effect, resulting in low genetic diversity within and between individuals. Here, we show that the ancient asexual ostracod species Darwinula stevensoni has very low nucleotide sequence divergence in three nuclear regions. Differences in genetic diversity between embryos and adults furthermore indicate that up to half of the observed genetic changes in adults can be caused by somatic mutations. Likelihood permutation tests confirm the presence of gene conversion in the multi-copy internal transcribed spacer sequence, but reject rare or cryptic forms of sex as a general explanation for the low genetic diversity in D. stevensoni. Other special mechanisms (such as highly efficient DNA repair) might have been selected for in this ancient asexual to overcome the mutational load and Muller's ratchet. In this case, our data support these hypotheses on the prevalence of sex, even if the two extant ancient asexual groups (bdelloids and darwinulids) seem to follow opposite evolutionary strategies.