One of the most promising properties of lead halide perovskite nanocrystals (NCs) is their defect tolerance. It is often argued that, due to the electronic structure of the conduction and valence bands, undercoordinated ions can only form localized levels inside or close to the band edges (i.e., shallow traps). However, multiple studies have shown that dangling bonds on surface Br- can still create deep trap states. Here, we argue that the traditional picture of defect tolerance is incomplete and that deep Br- traps can be explained by considering the local environment of the trap states. Using density functional theory calculations, we show that surface Br- sites experience a destabilizing local electrostatic potential that pushes their dangling orbitals into the bandgap. These deep trap states can be electrostatically passivated through the addition of ions that stabilize the dangling orbitals via ionic interactions without covalently binding to the NC surface. These results shed light on the formation of deep traps in perovskite NCs and provide strategies to remove them from the bandgap.