The structural and electronic properties of the complex tetrahedral structures B-8 (or ‘‘BC8,’’ bcc with 8 atoms per cell) and T-12 (or ‘‘ST12,’’ simple tetragonal with 12 atoms per cell) phases of silicon and carbon are computed with ab initio density-functional calculations of the energy, pressure, and enthalpy. For silicon, the B-8 and T-12 phases are found to be metastable, consistent with their formation during pressure reduction in high-pressure experiments. Energies of both structures are close to that of amorphous silicon. T-12 has an indirect gap larger than diamond-structure Si whereas B-8 is semimetallic. For carbon, the B-8 phase is found to be stable, relative to diamond and all previously calculated metallic phases, above pressures of 12 Mbar. This represents a new limit for the stability of diamond.