Face transplantation - or, more properly, facial allograft transplantation (FAT) - generates much public interest and academic debate. In this paper, we suggest that it is up to opponents of FAT to make the case for its impermissibility. We allow that there is a number of apparently strong arguments that might be deployed against FAT. However, all but one of these turn out not to be compelling after examination. The remaining argument is not so easily dismissed - but its central point is fairly workaday and certainly does not tell us anything about FAT in particular. Therefore, qua argument about facial transplant surgery, it fails to hit its target. Overall, we conclude that a compelling case against FAT remains to be made.