Involute gear sets are being produced through a variety of cutting tools and generation methods in a number of pressure angle and whole depth systems with 20–2.25 m being the most common. Positive addendum modifications (profile shifts) are also common particularly because the resulting teeth are stronger, although at the expense of the contact ratio, scoring resistance and pitting resistance. This paper discusses the effect of combined addendum modifications and changes in nominal tooth thickness of meshing gears on the minimization of the root bending stress. The tooth mesh-strength problem is treated as non-dimensional, which substantially reduces computational time as well as the total number of design variables. Instead of modeling the loaded gear tooth and running a numerical method (i.e. FEM) to calculate the maximum root stress at every iterative step of the optimization procedure, the stress is calculated by interpolation of tabulated values, which were calculated previously for different combinations of the design parameters. Significant stress reduction was achieved in this way as was confirmed experimentally with photoelasticity.