ABSTRACT The abundance of the faintest galaxies provides insight into the nature of dark matter and the process of dwarf galaxy formation. In the LCDM scenario, low-mass haloes are so numerous that the efficiency of dwarf formation must decline sharply with decreasing halo mass in order to accommodate the relative scarcity of observed dwarfs and satellites in the Local Group. The nature of this decline contains important clues to the mechanisms regulating the onset of galaxy formation in the faintest systems. We explore here two possible models for the stellar mass (M*)–halo mass (M200) relation at the faint end, motivated by some of the latest LCDM cosmological hydrodynamical simulations. One model includes a sharp mass threshold below which no luminous galaxies form, as expected if galaxy formation proceeds only in systems above the hydrogen-cooling limit. In the second model, M* scales as a steep power law of M200 with no explicit cut-off, as suggested by recent semi-analytical work. Although both models predict satellite numbers around Milky Way-like galaxies consistent with current observations, they predict vastly different numbers of ultrafaint dwarfs and of satellites around isolated dwarf galaxies. Our results illustrate how the satellite mass function around dwarfs may be used to probe the M*–M200 relation at the faint end and to elucidate the mechanisms that determine which low-mass haloes ‘light up’ or remain dark in the LCDM scenario.