The remarkable recent creation of two proteins that fold into two completely different and stable structures, exhibit different functions, yet differ by only a few amino acids poses a conundrum to those hoping to understand how sequence encodes structure. Here, computer modeling uniquely allows the characterization of not only the native structure of each minimally different sequence but also systems in which each sequence was modeled onto the fold of the alternate sequence. The reasons for the different structural preferences of two pairs of highly similar sequences are explored by a combination of structure analyses, comparison of potential energies calculated from energy-minimized single structures and trajectories produced from molecular dynamics simulations, and application of a novel method for calculating free energy differences. The sensitivity of such analyses to the choice of force field is also explored. Many of the hypotheses proposed on the basis of the nuclear magnetic resonance model structures of the proteins with 95% identical sequences are supported. However, each level of analysis provides different predictions regarding which sequence-structure combination should be most favored, highlighting the fact that protein structure and stability result from a complex combination of interdependent factors.