A method of fabricating an interconnection level of conductive lines and connecting vias separated by insulation for integrated circuits and substrate carriers for semiconductor devices using a reverse damascene in the formation of the conductive lines and vias. A conductive line pattern is first used to etch completely through the layer to form conductive line openings. The openings are completely filled with a conductive material and planarized so that the surfaces of the conductive material and the insulating layer are coplanar. A via pattern is aligned perpendicular to the conductive lines and the conductive material is etched half way through the conductive lines in other than the areas covered by the via pattern. The openings thus created in the upper portion of the conductive lines are filled with insulating material to complete the dual damascene interconnection level with the conductive lines in the lower portion of the insulating layer and upwardly projecting vias in the upper portion of the layer. In addition, a triple damascene layer is formed by starting with an insulating layer about one-third thicker than normal and by combining the standard dual damascene method with the above described method. The resulting interconnection level structure comprises conductive lines having upwardly and downwardly projecting vias.