Extracting kinetic models from single molecule data is an important route to mechanistic insight in biophysics, chemistry, and biology. Data collected from force spectroscopy can probe discrete hops of a single molecule between different conformational states. Model extraction from such data is a challenging inverse problem because single molecule data are noisy and rich in structure. Standard modeling methods normally assume (i) a prespecified number of discrete states and (ii) that transitions between states are Markovian. The data set is then fit to this predetermined model to find a handful of rates describing the transitions between states. We show that it is unnecessary to assume either (i) or (ii) and focus our analysis on the zipping/unzipping transitions of an RNA hairpin. The key is in starting with a very broad class of non-Markov models in order to let the data guide us toward the best model from this very broad class. Our method suggests that there exists a folding intermediate for the P5ab RNA hairpin whose zipping/unzipping is monitored by force spectroscopy experiments. This intermediate would not have been resolved if a Markov model had been assumed from the onset. We compare the merits of our method with those of others. © 2014 American Chemical Society.