The phenomenon of overlapping of various sequence messages in genomes is a puzzle for evolutionary theoreticians, geneticists, and sequence researchers. The overlapping is possible due to degeneracy of the messages, in particular, degeneracy of codons. It is often observed in organisms with a limited size of genome, possessing polymerases of low fidelity. The most accepted view considers the overlapping as a mechanism to increase the amount of information per unit length. Here we present a model that suggests direct evolutionary advantage of the message overlapping. Two opposing drives are considered: (a) reduction in the amount of vulnerable points when the overlapping of two messages involves common critical points and (b) cumulative compromising cost of coexistence of messages at the same site. Over a broad range of conditions the reduction of the target size prevails, thus making the overlapping of messages advantageous.