Localized states on undercoordinated atoms at the surface of a quantum dot (QD) can become electron or hole traps when the atomic orbitals involved fall within the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap of the material. Therefore, QDs of more covalent materials are predicted to be more sensitive to trap-state formation. Here, we analyze the relation between the presence of undercoordinated surface atoms and the formation of localized trap states for InP QDs by means of density functional theory. We argue that the requirement of charge neutrality limits the possible shapes cation-rich InP QDs can take, among which small cuboctahedrons and tetrahedrons of any size. We thus select both structures as InP model QDs and show that a complete InCl3 surface passivation results in an electronic structure with a clean, delocalized HOMO–LUMO gap in either case. Upon removal of InCl3 formula units from the InP cuboctahedron, hole traps linked to 2-coordinated surface P can form, a behavior similar to that of CdSe QDs. On the other hand, InCl3 displacement from the InP tetrahedron can lead to hole and electron traps, related to 2- or 3-coordinated surface P and 2-coordinated surface In, respectively. Since we obtain a very similar electronic structure of pristine InP and CdSe cuboctahedrons, we argue that the concept of ionicity provides little guidance to understand the enhanced sensitivity of InP to trap-state formation. Therefore, more apt descriptors are needed to predict the energetic position of atomic orbitals of uncoordinated atoms relative to the delocalized band-edge states.