  We discuss two mechanisms that could result in an enhancement of the mass
transfer rate during outbursts of dwarf novae and soft X-ray transients: the
hot outer disc rim itself could heat the L1 point and scattered radiation by
optically thin outflowing matter could also heat L1 significantly. We determine
quantitatively the increase of the mass transfer rate resulting from an extra
heating. During outbursts, the disc edge heats up the upper layer of the
secondary with a flux of the order of the intrinsic stellar flux. This probably
has no large effect on the mass transfer rate. In soft X-ray transients, the
environing medium of the disc (corona+wind) could back-scatter a certain
fraction of the accretion luminosity toward L1. Since soft X-ray transients
reach high luminosities, even a low efficiency of this effect could yield a
significant heating of L1, whereas we show that in dwarf novae this effect is
negligible. Initially the incoming radiation does not penetrate below the
photosphere of the secondary. Depending on the heating efficiency, which has to
be determined, the mass transfer rate could be significantly increased (~x100).
