In this talk I will discuss models of two-dimensional gravity that resolve the factorization puzzle and have a discrete spectrum, whilst retaining a semiclassical description. A novelty of these models is that they contain non-trivially correlated spacetime branes or, equivalently, nonlocal interactions in their action. Demanding factorization fixes almost all brane correlators, and the exact geometric expansion of the partition function collapses to only two terms: the black hole saddle and a subleading "half-wormhole" geometry, whose sum yields the desired discrete spectrum. Non-perturbatively, the correlated branes are a certain multitrace interaction and I will show how it results in a factorizing theory with discrete spectrum. I will end with a few comments on the relevance of wormholes and higher dimensions.