We construct non-supersymmetric, localized black holes in Type IIB supergravity on AdS3x S^3 x T^4. They appear in the spectrum immediately above the energy of global AdS3 and up to a finite fraction of the central charge. This range is outside the universal predictable range of the modular bootstrap in large-c CFT 2. We show that these localized black holes coexist with the BTZ solution, and dominate it in the microcanonical ensemble. As such, they provide a candidate for the endpoint of the BTZ instability at low energies. We find that our new geometries have almost the same entanglement entropy as the BTZ black hole, despite the very different horizon structures. However, they can be distinguished by non-minimal extremal surfaces, which reveal finer details of the microstructure.