  Very faint X-ray binaries appear to be transient in many cases with peak
luminosities much fainter than that of usual soft X-ray transients, but their
nature still remains elusive. We investigate the possibility that this
transient behaviour is due to the same thermal/viscous instability which is
responsible for outbursts of bright soft X-ray transients, occurring in
ultracompact binaries for adequately low mass-transfer rates. More generally,
we investigate the observational consequences of this instability when it
occurs in ultracompact binaries. We use our code for modelling the
thermal-viscous instability of the accretion disc, assumed here to be hydrogen
poor. We also take into account the effects of disc X-ray irradiation, and
consider the impact of the mass-transfer rate on the outburst brightness. We
find that one can reproduce the observed properties of both the very faint and
the brighter short transients (peak luminosity, duration, recurrence times),
provided that the viscosity parameter in quiescence is slightly smaller
(typically a factor of between two and four) than in bright soft X-ray
transients and normal dwarf nova outbursts, the viscosity in outburst being
unchanged. This possibly reflects the impact of chemical composition on
non-ideal MHD effects affecting magnetically driven turbulence in poorly
ionized discs.
