Abstract 1991T-like supernovae are the luminous, slow-declining extreme of the Branch shallow-silicon (SS) subclass of Type Ia supernovae. They are distinguished by extremely weak Ca ii H & K and Si ii λ6355 and strong Fe iii absorption features in their optical spectra at pre-maximum phases, and have long been suspected to be over-luminous compared to normal Type Ia supernovae. In this paper, the pseudo-equivalent width of the Si ii λ6355 absorption obtained at light curve phases from ≤ +10 days is combined with the morphology of the i-band light curve to identify a sample of 1991T-like supernovae in the Carnegie Supernova Project II. Hubble diagram residuals show that, at optical as well as near-infrared wavelengths, these events are over-luminous by ∼0.1–0.5 mag with respect to the less extreme Branch SS (1999aa-like) and Branch core-normal supernovae with similar B-band light-curve decline rates.