Pedestal and global plasma parameters are compared in ELMy H-mode discharges from ASDEX Upgrade (AUG), DIII-D, JET and JT-60U with varying input power and current profiles. Both electron and ion pedestal pressures are studied. The increase in pedestal pressure (pPED) with power is continuous, reflecting the continuous transition from "standard H-mode" to "improved confinement scenario". Higher pPED than in standard H-modes are found in improved H-modes in AUG and in JT-60U high bpol H-modes at q95 = 6.5. In AUG improved H-modes pPED increases with power due to an increase of both pedestal top density and temperature. In DIII-D pPED increases primarily due to an increase of the pedestal temperature, through an increase in width of the Te ETB and an increase of both width and gradient of the Ti ETB. For AUG the confinement improvement at high input power is due in part to increased core stored energy and in part to increased pedestal stored energy, while in DIII-D hybrid discharges it is due to increased core confinement. In JT-60U high bpol H-modes at q95 = 6.5 and high d the improved confinement is due to an increase of WPED, while in reversed shear H-modes to an increase of Wcore. In JET hybrid discharges at 1.4MA Wth increases with power and d due to an increase of WPED. In all four tokamaks improved edge stability is correlated to increasing total bpol and H98(y,2) increases with pedestal bpol.