Here, we present generalized rules underlying band inversiondriven warping and high valley degeneracy which hold true in all topological insulators. There are two conditions under which band warping occurs: (i) bands must be sufficiently inverted, and (ii) secondary bands (i.e. bands that are neither the conduction band edge nor valence band edge) must have opposite parity from, and be close in energy to, the band edges. If the conditions are satisfied, band inversion-induced warping can increase the valley degeneracy by 2-fold up to 48-fold depending on the symmetry of the structure. The study offers a novel band engineering perspective which leverages the electronic structure topology of a material.