We have used d. functional pseudopotential calcns. and mol. dynamics to predict new carbon structures of high stability. The new phases are strongly bound and involve the smallest radius nanotubes. It is possible to covalently link smallest/larger, smallest/smallest radius nanotubes together as well as larger nanotube/C20 1D-chains, resulting in extremely large interlinkage and consequent increase in the resistance to slippage. This procedure may enable the construction of extremely stiff nanotube bundles capable of making full use of the tensile properties of individual nanotubes, while enhancing the crystallinity of the material. Some of the carbon allotropes studied are the lowest energy non-diamond sp3 hybridized structures ever found.