Ohmic H modes have been achieved in ALCATOR C-MOD with toroidal fields up to BT ≈ 5.25 T and line averaged densities up to ne ≈ 1.4 × 1020 m-3 with less than 1 MW of input power. In ELM-free cases at lower toroidal fields, the energy confinement increases by at least 60% and the particle confinement increases by more than a factor of two. The ELM-free H modes appear to fit the threshold power scaling observed on other tokamaks, P/S (MW/m2)=4.4 × 10-3 neBT (1019 m-3.T), up to power densities of about 0.15 MW/m2. At higher toroidal fields, ELMy H modes were observed after the injection of lithium pellets at about half of the scaled threshold power density. All of these results were obtained with molybdenum plasma facing components and the ELM-free H modes were obtained without boronization or other wall coatings