Wave propagation through a slab dielectric waveguide with two periodic perturbations of the permittivity of very different amplitude but similar pitch is considered. The pitch of the weaker perturbation is chosen so that it lies in that part of the dispersion characteristic of the guide that is strongly distorted by the presence of the stronger perturbation. Coupled mode theory is used to analyse this situation, in which the spectral components of the index perturbation can no longer be taken to be independent of each other. Hence it is shown that the reflection bandwidth of the weak perturbation is narrowed by this particular configuration. The bandwidth decreases as the two pitches approach one another, but an effective limit on narrowing is imposed by the relatively strong side lobes of the reflectance of the strong pertyrbation.