A method for making a backlight unit for LCD displays is disclosed, involving a thin and flexible light transmissive sheet with first and second broad-area surfaces, and opposing first and second edges. A patterned light extraction area, comprising a two-dimensional pattern of microstructures, and a light mixing area, are formed on the sheet. A side-emitting LED strip is provided, with a flexible printed circuit, a linear array of side-emitting LED packages, and electrical contacts for power supply connection. The circuit's major surface is oriented parallel to the sheet and positioned in contact with one broad-area surface. A reflector is placed on one side of the sheet. The circuit and part of the light mixing area are covered with an opaque, heat-conductive housing. The light mixing area's width exceeds the sheet's thickness, and the light-emitting surface of each LED package is at least 1.5 times the sheet's thickness.