It is thought that many aspects of steady human locomotion under normal conditions can be predicted by appealing to the hypothesis that healthy humans roughly move in a manner that minimizes the metabolic cost of locomotion. While energy optimization with sufficiently realistic and complex models might be required for detailed quantitative predictions, we might obtain a deeper understanding of the qualitative effects of various model features on energetic optimal gaits by considering relatively simple models. Here, we consider four simple bipedal models with different leg architectures, combined with many different metabolic cost functions and muscle properties. Performing careful gait optimization on these many model permutations reveals simple underlying gait structure and similarity between the optimal gaits for substantially different models. We are also able to make a number of observations about the structure of the optimal gaits of the various models, many of which have not been previously noted.