In principle, evolutionary outcomes could be largely predicted if all of the relevant physicochemical variants of a particular protein function under selection were known and integrated into an appropriate physiological model. We have tested this principle by generating a family of variants of the tetracycline resistance protein TetX2 and identified the physicochemical properties most correlated with organismal fitness. Surprisingly, small changes in the Km(MCN), less than twofold, were sufficient to produce highly successful adaptive mutants over clinically relevant drug concentrations. We then built a quantitative model directly relating the in vitro physicochemical properties of the mutant enzymes to the growth rates of bacteria carrying a single chromosomal copy of the tet(X2) variants over a wide range of minocycline (MCN) concentrations. Importantly, this model allows the prediction of enzymatic properties directly from cellular growth rates as well as the physicochemical-fitness landscape of TetX2. Using experimental evolution and deep sequencing to monitor the allelic frequencies of the seven most biochemically efficient TetX2 mutants in 10 independently evolving populations, we showed that the model correctly predicted the success of the two most beneficial variants tet(X2)T280A and tet(X2)N371I. The structure of the most efficient variant, TetX2T280A, in complex with MCN at 2.7 Å resolution suggests an indirect effect on enzyme kinetics. Taken together, these findings support an important role for readily accessible small steps in protein evolution that can, in turn, greatly increase the fitness of an organism during natural selection.