Our analysis of the electronic structures of rock-salt IV-VI compounds shows that the mere existence of inverted bands is an insufficient condition for high valley degeneracy near the band edges. Instead, the k • p model of the L-point in rock-salt IV-VI compounds reveals that the degree to which the bands are inverted is a far more relevant property to consider. Our model predicts that a 6× increase in the valley degeneracy, from N V = 4 to N v = 24, can be achieved in rock-salt IV-VI compounds with inverted bands by tuning nearest-neighbor chemical interactions.