In the supersymmetric triplet (type-II) seesaw model, in which a single SU(2)_L-triplet couples to leptons, the high-energy neutrino flavour structure can be directly determined from the low-energy neutrino data. We show that even with such a minimal triplet content, leptogenesis can be naturally accommodated thanks to the resonant interference between superpotential and soft supersymmetry breaking terms.