The basic assumption is made, that definite conformations of mRNA molecules are important for their stability within the cytoplasma. These conformations are thought to be partly due to hydrogen bonds between appropriate bases arranged in “hairpins”. To check the idea that code degeneracy may have had a function in preservation of these mRNA conformations during evolution, amino acid sequences of various proteins were “retranslated” into hypothetical mRNAs. A computer program is described, which simulates the formation of secondary structures in these RNAs by selection of the degenerated nucleotides either at random or according to an optimizing procedure. The results of numerous computer runs indicate that in no case the random selection of the degenerated nucleotides leads to a second structure of high stability. Therefore a selection scheme different from a random replacement of the undefinite degenerated positions has to be postulated, provided that stability of mRNA conformations was advantageous in the course of evolution. Computations by an optimizing procedure applied to different numbers ( n) of nucleotides for the initial hairpins ( n = 25 to n = 100) result in optimal structures of the highest free energy at 60–70 nucleotides.