In JT-60U H-mode plasmas, giant (type I) ELMs disappear and minute grassy ELMsappear when triangularity δ, edge safety factor q95 and βpare high enough. Complete suppression of giant ELMs was observed atδ≳0.45, q95≳6 and βp≳1.6. At higher δ(0.54), giant ELMs can disappear at a lower q95 (~4.0). In thegrassy ELMy H-mode, edge temperature and pressure can be higher than those ingiant ELMy H-mode and a favourable confinement can be sustained without anincrease of the impurity concentration. An edge stability analysis suggeststhat the edge plasma is accessing the second stability regime of the high nballooning mode in the grassy ELMy discharges.