Philosophers disagree how abstract, theoretical principles can be applied to instances. This paper generates a puzzle for law theorists, causal theorists and inductivists alike. Intractability can force scientists to use a "semi-empirical" method, in which some of an equation's theoretically-determinable parameters are replaced with values taken directly from the data. This is not a purely deductive or inductive process, nor does it involve causes and capacities in any simple way (Humphreys 1995). I argue the predictive successes of such methods require (...) us to reanalyze our views about the nature of prediction, the status of models, and the goal(s) of science. When laws and experimental evidence are neither individually nor jointly sufficient for prediction, models become the locus of understanding. I analyze an historically important debate about the use of semi-empirical methods to construct potential energy surfaces. (shrink)