  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 $\lambda6355$ 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 $\lambda$6355 absorption
obtained at light curve phases from $\leq+10$ 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 $\sim$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.
