  We perform a detailed analysis of thermal leptogenesis in the framework of
seesaw models which approximately conserve lepton number. These models are
known to allow for large Yukawa couplings and a low seesaw scale in agreement
with neutrino mass constraints, and hence to lead to large lepton flavour
violating rates that can be probed experimentally. Although large Yukawa
couplings lead to (inverse) decay rates much larger than the Hubble expansion
rate, we show that the leptogenesis washout induced is generically small if the
mass splitting between the right-handed neutrinos is small enough. As a result,
large lepton flavour violating rates are compatible with successful
leptogenesis. We emphasize that this scenario does not require any particular
flavour structure. A small splitting is natural and radiatively stable in this
context because it is protected by the lepton number symmetry.
