A method of thinning dice or integrated circuit chips used in producing lightweight packaged electronic systems, such as HDI circuits and systems produced therefrom provides for positioning dice in a die carrier layer that allows for easy separation from the dice after completion of the die thinning step. A holding layer is then attached to the die carrier layer for ease of attaching it to a material removal device, such as a lapping machine or an ultrasonic milling machine. A portion of the die carrier layer, along its exposed side, is then removed by the material removal device as a consequence of removal, by the material removal device, of an expendable portion of the dice positioned within the die carrier layer. The holding layer and the die carrier layer are then separated from the thinned dice by a conventional method, such as chemical etching, solvent soaking or induction heating. The thinned dice are significantly lighter than their original weight and their uniform thickness makes them well suited for mass produced lightweight electronic systems and flexible assemblies, such as HDI circuits.