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 irradiat
ion of the disc by X-rays from the inner regions is included. We present th
e first numerically reliable, physically consistent calculations of the out
burst cycles which include the effects of accretion disc irradiation. The d
ecay from outburst is governed by irradiation, as pointed out by King & Rit
ter (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 recurr
ence times and quiescent X-ray luminosities of SXTs still require the inner
disc to be replaced by another type of ow in quiescence, presumably a hot
advection dominated accretion ow (ADAF). We include the effects of such tru
ncation and show that the resulting lightcurves are conclusively similar to
those of SXTs like A0620-00. We conclude that the two-alpha disc instabili
ty model provides an adequate description of the outbursts of SXTs when bot
h truncation and irradiation are included. The values for the viscosities i
n outburst and in quiescence are comparable to those used in CVs. We discus
s the model in the context of present observations.