  Very faint X-ray binaries (VFXBs), defined as having peak luminosities Lx of
10^34-10^36 erg/s, have been uncovered in significant numbers, but remain
poorly understood. We analyse three published outburst light curves of two
transient VFXBs using the exponential and linear decay formalism of King and
Ritter (1998). The decay timescales and brink luminosities suggest orbital
periods of order 1 hour. We review various estimates of VFXB properties, and
compare these with suggested explanations of the nature of VFXBs. We suggest
that: 1) VFXB outbursts showing linear decays might be explained as partial
drainings of the disc of "normal" X-ray transients, and many VFXB outbursts may
belong to this category; 2) VFXB outbursts showing exponential decays are best
explained by old, short-period systems involving mass transfer from a low-mass
white dwarf or brown dwarf; 3) persistent (or quasi-persistent) VFXBs, which
maintain an Lx of 10^34-10^35 erg/s for years, may be explained by
magnetospheric choking of the accretion flow in a propeller effect, permitting
a small portion of the flow to accrete onto the neutron star's surface. We thus
predict that (quasi-)persistent VFXBs may also be transitional millisecond
pulsars, turning on as millisecond radio pulsars when their Lx drops below
10^32 erg/s.
