The intricate functions of membrane proteins would not be possible without bends or breaks that are remarkably common in transmembrane helices. The frequent helix distortions are nevertheless surprising because backbone hydrogen bonds should be strong in an apolar membrane, potentially rigidifying helices. It is therefore mysterious how distortions can be generated by the evolutionary currency of random point mutations. Here we show that we can engineer a transition between distinct distorted helix conformations in bacteriorhodopsin with a single-point mutation. Moreover, we estimate the energetic cost of the conformational transitions to be smaller than 1 kcal/mol. We propose that the low energy of distortion is explained in part by the shifting of backbone hydrogen bonding partners. Consistent with this view, extensive backbone hydrogen bond shifts occur during helix conformational changes that accompany functional cycles. Our results explain how evolution has been able to liberally exploit transmembrane helix bending for the optimization of membrane protein structure, function, and dynamics.