We report on the second family of layered perovskite white-light emitters with improved photoluminescence quantum efficiencies (PLQEs). Upon near-ultraviolet excitation, two new Pb-Cl and Pb-Br perovskites emit broadband "cold" and "warm" white light, respectively, with high color rendition. Emission from large, single crystals indicates an origin from the bulk material and not surface defect sites. The Pb-Br perovskite has a PLQE of 9%, which is undiminished after 3 months of continuous irradiation. Our mechanistic studies indicate that the emission has contributions from strong electron-phonon coupling in a deformable lattice and from a distribution of intrinsic trap states. These hybrids provide a tunable platform for combining the facile processability of organic materials with the structural definition of crystalline, inorganic solids.