A method is used to make a laser-ablatable element for direct laser engraving that has a laser-ablatable, relief-forming layer that has a relief-image forming surface and a bottom surface. The relief-forming layer can be prepared by applying multiple formulations. Each formulation comprises a coating solvent, a laser-ablatable polymeric binder, and an infrared radiation absorbing compound. The infrared radiation absorbing compound concentration in the resulting sub-layers is different in each adjacent pair of sub-layers so that the concentration is always greater in each pair sub-layer that is closer to the substrate, and the concentration is progressively greater in the sub-layers as they are closer to the substrate after the coating solvent is removed, wherein the multiple sub-layers provide a relief-forming layer so that the sub-layer farthest from the substrate provides a relief-image forming surface.