We have developed a new technique of mineral substitution that accurately predicts the change in rock stiffness upon changes in the elastic properties of the rock mineral frame, assuming no changes in the microstructure or mineral volume fraction. The method is rigorous, the results are realizable, and the predictions are always within bounds. We have applied mineral substitution to separate the effects of composition (mineralogy and pore fill) on the rock stiffness from the effects of microstructure, i.e., porosity and pore shape. Application of mineral substitution on laboratory measured data sets of effective moduli (sandstones, limestones, and dolomites) revealed that if the original minerals making up the frame of sandstones (predominantly quartz) were replaced (or substituted) with calcite mineral properties, the newly predicted P- () and S-wave velocity () trends for the modified sandstones were very similar to the previously observed quadratic - empirical trends for limestones. Similarly, the - trends for modified limestones, with original minerals replaced by quartz mineral properties, were very similar to the observed linear - empirical trends for sandstones. The remaining minor differences between the modified and previously observed - trends might be attributed to the differences in rock microstructure. These findings are striking and suggest that - trends of natural rocks are dominated by mineralogy and the effects of microstructure are minor. We also found new - trends for rocks composed of various minerals, including zeolite, feldspar, pyrite, alpha-cristobalite, and halite.