Looking for Nm* values for humans I stumbled across an interesting paper, Estimating sex-specific processes in human populations: Are XY-homologous markers an effective tool?:
...To test this idea, we analyzed XY-homologous microsatellite diversity in 33 human populations from Africa, Asia and Europe. Interpopulation comparisons suggest that the generally discordant pattern of genetic variation observed for X- and Y-linked markers could be an outcome of sex-specific migration processes (mfemales/mmales ~ 3) or sex-specific demographic processes (Nfemales/Nmales ~ 11) or a combination of both....
Basically the authors were looking at diversity on homologous markers on the X & Y chromosomes. Previously researchers had compared mtDNA (female) and Y (male) lineages, but the authors point out that the comparison using these two regions of the genome might be problematic (e.g., mtDNA is subject to its own peculiarities such as high mutational rate, and might not be as neutral as we assume). The diversity ...