The coupling-wave model is applied to obtain an exact analytic solution to the problem of diffraction of a plane electromagnetic wave from a nonharmonic Bragg grating with a spatially modulated refractive index n(z) = n 0 + Δn(z)cos(2πz/d + ϕ). Apodization for such gratings is described by continuous functions of the form n(z) = ±Δn/[1 ∓ n(z ∓ L/2)] (d, L, ϕ, and Δn = const are the period, length, phase, and amplitude of a grating, respectively) or piecewise-continuous symmetric and antisymmetric analogues constructed from these functions. Conditions ensuring suppression of oscillations in the reflection and transmission spectra of these gratings are found. It is shown that, when the coupling factor of a grating is antisymmetric, a narrow transparency band is observed within the forbidden transmission band located near a Bragg resonance. An analytic expression is obtained for the dependence of the width of the transparency band on the grating’s parameters. Gratings with an antisymmetric coupling factor can be used in narrowband frequency-selective Bragg transmission filters.