  We reanalyse leptogenesis via the out-of-equilibrium decay of the lightest
right-handed neutrino in type II seesaw scenarios, taking into account
flavour-dependent effects. In the type II seesaw mechanism, in addition to the
type I seesaw contribution, an additional direct mass term for the light
neutrinos is present. We consider type II seesaw scenarios where this
additional contribution arises from the vacuum expectation value of a Higgs
triplet, and furthermore an effective model-independent approach. We
investigate bounds on the flavour-specific decay asymmetries, on the mass of
the lightest right-handed neutrino and on the reheat temperature of the early
universe, and compare them to the corresponding bounds in the type I seesaw
framework. We show that while flavour-dependent thermal type II leptogenesis
becomes more efficient for larger mass scale of the light neutrinos, and the
bounds become relaxed, the type I seesaw scenario for leptogenesis becomes more
constrained. We also argue that in general, flavour-dependent effects cannot be
ignored when dealing with leptogenesis in type II seesaw models.
