  We study the prospect of explaining the outbursts of Soft X-ray Transients
(SXTs) by the thermal-viscous instability in a thin disc. This instability is
linked to hydrogen ionization and is significantly changed when irradiation of
the disc by X-rays from the inner regions is included. We present the first
numerically reliable, physically consistent calculations of the outburst cycles
which include the effects of accretion disc irradiation. The decay from
outburst is governed by irradiation, as pointed out by King & Ritter (1998),
leading to slow exponential decays. At the end of the outburst, the disc is
severely depleted, which lengthens the time needed to rebuild mass to the
critical density for an outburst. Despite this, the long recurrence times and
quiescent X-ray luminosities of SXTs still require the inner disc to be
replaced by another type of flow in quiescence, presumably a hot advection
dominated accretion flow (ADAF). We include the effects of such truncation and
show that the resulting lightcurves are conclusively similar to those of SXTs
like A0620-00. We conclude that the two-alpha disc instability model provides
an adequate description of the outbursts of SXTs when both truncation and
irradiation are included. The values for the viscosities in outburst and in
quiescence are comparable to those used in CVs. We discuss the model in the
context of present observations.
