We study the fluctuation spectrum of linearized gravity around non-fine-tuned branes. We focus on the case of an AdS4 brane in AdS5. In this case, for small cosmological constant, the warp factor near the brane is essentially that of a Minkowski brane. However, far from the brane, the metric differs substantially. The space includes the AdS5 boundary, so it has infinite volume. Nonetheless, for sufficiently small AdS4 cosmological constant, there is a bound state graviton in the theory, and four-dimensional gravity is reproduced. However, it is a massive bound state that plays the role of the four-dimensional graviton.