A dielectric in an integrated circuit is formed by creating oriented cylindrical voids in a conventional dielectric material. Preferably, voids are formed by first forming multiple relatively long, thin carbon nanotubes perpendicular to a surface of an integrated circuit wafer, depositing a conventional dielectric on the surface surrounding the carbon nanotubes, and then removing the carbon nanotubes to produce the voids. A layer of dielectric and voids thus formed can be patterned or otherwise processed using any of various conventional processes. Recesses formed in the dielectric for conductors are lined with a non-conformal dielectric film to seal the voids. The use of a conventional dielectric material having numerous air voids substantially reduces the dielectric constant, leaving a dielectric structure which is both structurally strong and can be constructed compatibly with conventional processes and materials.