DNA molecules contain a second layer of information on top of the classical genetic information. This second layer is geometrical/mechanical in nature and guides the folding of DNA molecules inside cells. With the help of a new Monte Carlo technique, Mutation Monte Carlo, and of graph theory we demonstrate that the degeneracy of the genetic code allows for multiplexing of the two information layers. We specifically show that mechanical cues on the DNA molecule can place nucleosomes with single base-pair resolution anywhere on the genome of baker’s yeast. This suggests that there is plenty of space for other layers of information as e.g. the translation speed in ribosomes - important for the co-translational folding of proteins. We show that it is indeed possible to design synonymous mutations to reposition nucleosomes on genes under the additional constraint of keeping the translation speed pattern nearly intact.