We have analyzed Rossi X-Ray Timing Explorer pointed observations of the outbursts of black hole and neutron star soft X-ray transients in which an initial low/hard state, or ``island'' state, followed by a transition to a softer state was observed. In three sources-the black hole transient XTE J1550-564, the neutron star transient Aquila X-1, and the quasi-persistent neutron star low-mass X-ray binary 4U 1705-44-two such outbursts were found. We find that the flux of the soft X-ray peak, which lags the hard X-ray peak by a few days to several weeks, scales with the flux of the hard X-ray peak. We conclude that we are able to predict the soft X-ray outburst peak flux based on the ``preceding'' hard X-ray peak flux, implying an early setup o...