Since it is uncertain if ITER operation is compatible with type-I ELMs, the study of alternative H-mode pedestals is an urgent issue. This paper reports on experiments on JET aiming to find scenarios with small ELMs and good confinement, such as the type-II ELMs in ASDEX Upgrade, the enhanced Dalpha H-mode in Alcator C-mod or the grassy ELMs in JT-60U. The study includes shape variations, especially the closeness to a double-null configuration, variations of q95, density and beta poloidal. Hmode pedestals without type-I ELMs have been observed only at the lowest currents (<1.2MA), showing similarities to the observations in the devices mentioned above. These are discussed in detail on the basis of edge fluctuation analysis. For higher currents, only the mixed type-I/II scenario is observed. Although the increased inter-ELM transport reduces the type-I ELM frequency, a single type-I ELM is not significantly reduced in size. Obviously, these results do question the accessibility of such small ELM scenarios on ITER, except perhaps the high beta-poloidal scenario at higher q95, which could not be tested at higher currents at JET due to limitations in heating power.