An empirical model and an ab initio calculation of the bulk moduli for covalent solids are used to suggest possible new hard materials. The empirical model indicates that hypothetical covalent solids formed between carbon and nitrogen are good candidates for extreme hardness. A prototype system is chosen and a first principles pseudopotential total energy calculation on the system is performed. The results are consistent with the empirical model and show that materials like the prototype can have bulk moduli comparable to or greater than diamond. It may be possible to synthesize such materials in the laboratory.