The paper investigates measures of explanatory power and how to define the inference schema “Inference to the Best Explanation” (IBE). It argues that these measures can also be used to quantify the systematic power of a hypothesis and defines the inference schema “Inference to the Best Systematization” (IBS). It demonstrates that systematic power is a fruitful criterion for theory choice and that IBS is truth-conducive. It also shows that even radical Bayesians must admit that systematic power is an integral component of Bayesian reasoning. Finally, the paper puts the achieved results in perspective with van Fraassen’s famous criticism of IBE.