  The outbursts of low mass X-ray binaries are prolonged relative to those of
dwarf nova cataclysmic variables as a consequence of X-ray irradiation of the
disc. We show that the time-scale of the decay light curve and its luminosity
at a characteristic time are linked to the radius of the accretion disc. Hence
a good X-ray light curve permits two independent estimates of the disc radius.
In the case of the milli-second pulsars SAX J1808.4-3658 and XTE J0929-314 the
agreement between these estimates is very strong. Our analysis allows new
determinations of distances and accretion disc radii. Our analysis will allow
determination of accretion disc radii for sources in external galaxies, and
hence constrain system parameters where other observational techniques are not
possible. We also use the X-ray light curves to estimate the mass transfer
rate. The broken exponential decay observed in the 2002 outburst of SAX
J1808.4-3658 may be caused by the changing self-shadowing of the disc.
