The majority of aneuploid fetuses are spontaneously miscarried. Nevertheless, some aneuploid individuals survive despite the strong genetic insult. Here, we investigate if the survival probability of aneuploid fetuses is affected by the genome-wide burden of slightly deleterious variants. We analyzed two cohorts of live-born Down syndrome individuals (388 genotyped samples and 16 fibroblast transcriptomes) and observed a deficit of slightly deleterious variants on Chromosome 21 and decreased transcriptome-wide variation in the expression level of highly constrained genes. We interpret these results as signatures of embryonic selection, and propose a genetic handicap model whereby an individual bearing an extremely severe deleterious variant (such as aneuploidy) could escape embryonic lethality if the genome-wide burden of slightly deleterious variants is sufficiently low. This approach can be used to study the composition and effect of the numerous slightly deleterious variants in humans and model organisms.