While study of the D1D5 system has shown significant agreement with expected black hole behavior in the classical limit, a full microscopic description of black hole formation and subsequent evaporation is still missing. This process is mirrored by thermalization in the CFT dual. Study of this dual begins at a conjectured 'orbifold point' in the moduli space where the CFT is particularly simple, but an account of thermalization requires deforming the theory away from this simple point. I present an ongoing analysis of this deformation, including a complete account of all first-order deformations, a particularly-simple second-order deformation, and a few generalizations for arbitrary orders of the deformation's twist component.