Owing to optical refraction, external rays that are incident upon a high-refractive-index medium fall within a small internal cone angle. A one-dimensionally periodic Bragg structure can reflect over an angular acceptance range that is greater than the small internal refraction cone, if the internal refractive-index contrast is sufficient. Thus Winn et al. [Opt. Lett. (to be published)] charted the range of refractive indices at which omnidirectional external reflection occurs. A wide spectral gap requires a high-index contrast. It is proposed that, by chirping or grading the periodicity of the structure, one can cover an arbitrarily wide spectral range with only a modest index contrast and, furthermore, that arbitrary spectral shapes can be produced. The graded-periodicity approach requires only a modest index contrast, provided that the average refractive index is >2 .