A closed air gap interconnect structure is described. The structure includes discrete regions of a permanent support dielectric under the interconnect lines so that the lines are substantially surrounded by air except for the discrete regions of the support dielectric and the optional interconnect vias located underneath. The lines and the lateral gap between them are straddled on top by a cap layer so that a closed air gap is formed. Several embodiments of this structure and methods to fabricate the same are also described.