We construct time-dependent models of accretion discs around black holes and neutron stars .
We investigate the effect of evaporating the disc inner regions during quiescence on the predictions of the Disc Instability Model ( DIM ) for these systems .
We do not include irradiation of the disc in the models .

Removing the inner , most unstable parts of the accretion disc increases the predicted recurrence times .
However , DIMs with values of the viscosity parameter \alpha _ { hot } \sim 0.1 and \alpha _ { cold } \sim 0.02 ( typical of applications of the DIM to standard dwarf nova outbursts ) fail to reproduce the long recurrence times of SXTs ( unless we resort to fine-tuning of the parameters ) independent of the evaporation strength .
We show that models with evaporation and a smaller value of \alpha _ { cold } ( \sim 0.005 ) do reproduce the long recurrence times and the accretion rates at the level of the Eddington rate observed in outburst .
The large difference between the values of \alpha _ { hot } and \alpha _ { cold } , if confirmed when disc irradiation is included , suggests that several viscosity mechanisms operate in these accretion discs .

For some choices of parameters our models predict reflares during the decline from outburst .
They are a physical property of the model and result from a heating front forming in the wake of an initial cooling front and subsequent , multiple front reflections .
The reflares disappear in low– \alpha models where front reflection can not occur .