My aim in this article is to contribute to the larger project of assessing the relative merits of different theories of substance. An important preliminary step in this project is assessing the explanatory resources of one main theory of subs- tance, the so-called bundle theory. This article works towards such an assessment. I identify and explain three distinct explanatory challenges an adequate bundle theory must meet. Each points to a putative explanatory gap, so I call them the ex- planatory challenges. I consider three bundle-theoretic strategies for meeting these challenges. I argue that none of them goes very far. The upshot is that, absent other strategies for meeting the challenges, bundle theory involves a significant amount of stipulation. This black box makes bundle theory relatively weak with respect to its explanatory power—unless, of course, rival theories of substance are unable to do better.