Non-recombining populations should suffer from four classic population genetic disadvantages: (1) they cannot reverse Muller's Ratchet, the accumulation of deleterious mutations caused by genetic drift and mutation; (2) whenever the fix a favourable mutation they lose all unlinked favourable variants; (3) they tend to lose favourable mutations that are linked to deleterious mutations; and (4) their genetic loads can be quite high when deleterious mutations have synergistic effects. It is commonly assumed that inter-chromosomal recombination (independent assortment) can counter these phenomena, but this has been studied only for the genetic load case. In contrast, many studies have shown that recombination via crossing over can counter these phenomena. Here we first show that segregation alone can strongly decelerate Muller's Ratchet in diploids, i.e. that recombination is not the only way to do so. We then show that inter-chromosomal recombination can indeed deal with phenomena (1) to (3) above very effectively if the genome consists of a moderate number of chromosomes. Therefore, if the above advantages of genetic recombination played a large role in the initial success of eukaryotic sex, the crucial moment in the origin of sex might have been the evolution of inter-chromosomal recombination, i.e. the evolution of genome segmentation, segregation, and syngamy. Crossing over might have become established as a major recombinational device only later, eliminating the disadvantages of extensively segmented genomes.