Power requirements for maintaining sufficiently high confinement (i.e. normalized energy confinement time H98 ⩾ 1) in H-mode and its relation to H-mode threshold power scaling, Pth, are of critical importance to ITER. In order to better characterize these power requirements, recent experiments on the Alcator C-Mod tokamak have investigated H-mode properties, including the edge pedestal and global confinement, over a range of input powers near and above Pth. In addition, we have examined the compatibility of impurity seeding with high performance operation, and the influence of plasma radiation and its spatial distribution on performance. Experiments were performed at 5.4 T at ITER relevant densities, utilizing bulk metal plasma facing surfaces and an ion cyclotron range of frequency waves for auxiliary heating. Input power was scanned both in stationary enhanced Dα (EDA) H-modes with no large edge localized modes (ELMs) and in ELMy H-modes in order to relate the resulting pedestal and confinement to the amount of power flowing into the scrape-off layer, Pnet, and also to the divertor targets. In both EDA and ELMy H-mode, energy confinement is generally good, with H98 near unity. As Pnet is reduced to levels approaching that in L-mode, pedestal temperature diminishes significantly and normalized confinement time drops. By seeding with low-Z impurities, such as Ne and N2, high total radiated power fractions are possible, along with substantial reductions in divertor heat flux (>4×), all while maintaining H98 ∼ 1. When the power radiated from the confined versus unconfined plasma is examined, pedestal and confinement properties are clearly seen to be an increasing function of Pnet, helping to unify the results with those from unseeded H-modes. This provides increased confidence that the power flow across the separatrix is the correct physics basis for ITER extrapolation. The experiments show that Pnet/Pth of one or greater is likely to lead to H98 ⩾ 1 operation, and also that such a condition can be made compatible with a low-Z radiative impurity solution for reducing divertor heat loads to levels acceptable for ITER.