Investigating people's representations of categories of complicated objects is a difficult challenge, not least because of the large number of ways in which such objects can vary. To make progress we need to take advantage of the structure of object categories -- one compelling regularity is that object categories can be described by a small number of dimensions. We present Look-Ahead Monte Carlo with People, a method for exploring people's representations of a category where there are many irrelevant dimensions. This method combines ideas from Markov chain Monte Carlo with People, an experimental paradigm derived from an algorithm for sampling complicated distributions, with hybrid Monte Carlo, a technique that uses directional information to construct efficient statistical sampling algorithms. We show that even in a simple example, our approach takes advantage of the structure of object categories to make experiments shorter and increase our ability to accurately estimate category representations.