A bleachable composition, including an acid photogenerator and a near-infrared radiation-absorbing dye or pigment, is utilized in a method of migration imaging to prevent unwanted absorptions. This composition can be incorporated either in the thermoplastic imaging surface layer of the imaging element, in the marking particles applied to the element, or both. Alternatively, the components of the bleachable composition can be separated with one in the thermoplastic imaging surface layer and the other in the marking particles. After the imaging element is marked and exposed with near-infrared radiation, the bleachable composition causes exposed portions of the imaging element to be bleached. If further bleaching is needed, the element can subsequently be exposed with near-ultraviolet radiation.