The melt rates of fresh and saline drifting ice, heated from below, are examined using a one-dimensional ice/ocean model with high vertical resolution. The model is based on the conservation equations for heat, salt, and momentum and uses turbulence models to achieve closure. The model includes a low-Reynolds number turbulence model for the viscous region, coupled to a high-Reynolds number turbulence model for the outer boundary, and a discrete element approach to the parameterization of roughness. It is shown that the melt rate of drifting ice is sensitive to ice roughness and molecular salt diffusion, and it is found that bulk heat transfer coefficients vary within a rather narrow range in the examined interval.