We aim to characterise a sample of fast-declining Type Ia supernovae (SN Ia) using their bolometric and near-infrared (NIR) properties. Based on these properties, we find that fast-declining SN Ia separate into two categories based on their bolometric and NIR properties. The peak bolometric luminosity (Lmax), the phase of the first maximum relative to the optical, the NIR peak luminosity, and the occurrence of a second maximum in the NIR distinguish a group of very faint SN Ia. Fast-declining supernovae show a large range of peak bolometric luminosities (Lmax differing by up to a factor of ~8). All fast-declining SN Ia with Lmax < 0.3× 1043 erg s-1 are spectroscopically classified as 91bg-like and show only a single NIR peak. SNe with Lmax > 0.5× 1043 erg s-1 appear to smoothly connect to normal SN Ia. The total ejecta mass (Mej) values for SNe with enough late time data are ≲1 M⊙, indicating a sub-Chandrasekhar mass progenitor for these SNe. Key words: supernovae: general