New experimental data from the Alcator C-Mod tokamak are used to benchmark predictive modelling of the edge pedestal in various high-confinement regimes, contributing to greater confidence in projection of pedestal height and width in ITER and reactors. ELMy H-modes operate near stability limits for ideal peeling–ballooning modes, as shown by calculations with the ELITE code. Experimental pedestal width in ELMy H-mode scales as the square root of βpol at the pedestal top, i.e. the dependence expected from theory if kinetic ballooning modes (KBMs) were responsible for limiting the pedestal width. A search for KBMs in experiment has revealed a short-wavelength electromagnetic fluctuation in the pedestal that is a candidate driver for inter-edge localized mode (ELM) pedestal regulation. A predictive pedestal model (EPED) has been tested on an extended set of ELMy H-modes from C-Mod, reproducing pedestal height and width reasonably well across the data set, and extending the tested range of EPED to the highest absolute pressures available on any existing tokamak and to within a factor of three of the pedestal pressure targeted for ITER. In addition, C-Mod offers access to two regimes, enhanced D-alpha (EDA) H-mode and I-mode, that have high pedestals, but in which large ELM activity is naturally suppressed and, instead, particle and impurity transport are regulated continuously. Pedestals of EDA H-mode and I-mode discharges are found to be ideal magnetohydrodynamic (MHD) stable with ELITE, consistent with the general absence of ELM activity. Invocation of alternative physics mechanisms may be required to make EPED-like predictions of pedestals in these kinds of intrinsically ELM-suppressed regimes, which would be very beneficial to operation in burning plasma devices.