Results are presented of experiments carried out in JET with the Mark II divertor to study ELMy H modes at high density. In these experiments the effective ion mass of the plasma (pure hydrogen, deuterium and tritium), input power, plasma current and edge triangularity were varied. The variation of density was achieved by gas fuelling. The focus is on two main issues: the variation of global energy confinement with density and the scaling of the H mode pedestal. It is found that the density dependence in the ITER97-P(y) scaling is not confirmed by experiment when the density limit is approached. For the high density regime in ELMy H modes a density independent scaling is proposed that includes the plasma triangularity in the regression variables. The core energy content of the plasma is correlated to the edge pedestal parameters, consistently with a mixed Bohm-gyroBohm transport model for H mode plasmas. It is found that with type I ELMs, the edge pedestal pressure increases with the ion mass of the plasma, the input power and the edge magnetic shear. A scaling is derived for the pressure at the top of the edge pedestal which is consistent with a model where the pedestal width is assumed to be proportional to the ion gyro-radius and the pedestal gradient is limited by ideal MHD.