While Chandrasekhar-mass (M_Ch) models with a low ^56Ni yield can match the peak luminosities of fast-declining, 91bg-like Type Ia supernovae (SNe Ia), they systematically fail to reproduce their faster light-curve evolution. Here, we illustrate the impact of a low ejecta mass on the radiative display of low-luminosity SNe Ia, by comparing a sub-M_Ch model resulting from the pure central detonation of a C-O white dwarf (WD) to an M_Ch delayed-detonation model with the same ^56Ni yield of 0.12 M_⊙. Our sub-M_Ch model from a 0.90 M_⊙ WD progenitor has a ∼5 d shorter rise time in the integrated UV–optical–IR (uvoir) luminosity, as well as in the B band, and a ∼20 per cent higher peak uvoir luminosity (∼1 mag brighter peak M_B). This sub-M_Ch model also displays bluer maximum-light colours due to the larger specific heating rate, and larger post-maximum uvoir and B-band decline rates. The luminosity decline at nebular times is also more pronounced, reflecting the enhanced escape of gamma rays resulting from the lower density of the progenitor WD. The deficit of stable nickel in the innermost ejecta leads to a notable absence of forbidden lines of [Ni ii] in the nebular spectra. In contrast, the M_Ch model displays a strong line due to [Ni ii] 1.939 μm, which could in principle serve to distinguish between different progenitor scenarios. Our sub-M_Ch model offers an unprecedented agreement with optical and near-infrared observations of the 91bg-like SN 1999by, making a strong case for a WD progenitor significantly below the Chandrasekhar-mass limit for this event and other low-luminosity SNe Ia.