Many jet-substructure techniques, motivated by a heuristic picture of parton showering, define observables using tree-like structures fashioned out of a jet's constituents. As a given set of constituents could have come from many possible showering histories, substructure techniques use a physically motivated clustering algorithm (e.g. C/A or kT ) to chose one of the more probable of such histories to associate with a jet. Typically only one history is considered, even if there are many candidates which could reasonably be associated with the jet at hand. Unfortunately, considering only a single, somewhat arbitrarily chosen tree introduces an uncertainty on any measurement thus obtained. Here we propose that rather than assigning each jet a single tree, one should instead "sum over paths" and consider a weighted distribution of observables obtained from many plausible tree structures. The procedure we advocate is simple to implement on top of an existing substructure analysis, and we argue that it is in general useful for reducing the uncertainty of a substructure measurement. We explicitly demonstrate its utility for mass measurement and signal discovery/exclusion using jet pruning techniques, where we find the reduced uncertainties obtained are equivalent to a twofold gain in luminosity.