Methods of leveling ink on substrates and apparatuses useful in printing are provided. An exemplary embodiment of the methods includes irradiating ink disposed on a first surface of a porous substrate with radiation emitted by at least one flash lamp. The radiation flash heats the ink to at least a viscosity threshold temperature of the ink to allow the ink to flow laterally on the first surface to produce leveling of the ink. The ink is heated sufficiently rapidly that heat transfer from the ink to the substrate is sufficiently small during the leveling that ink at the substrate interface is cooled to a temperature below the viscosity threshold temperature thereby preventing any significant ink permeation into the substrate from the first surface.