Abstract We demonstrate that the modes of coupled cavities created in periodic waveguides can depend critically on the longitudinal shift between the cavities. In the absence of such shift, the modes feature symmetric or antisymmetric profiles, and their frequency splitting generally increases as the cavities are brought closer. We show that the longitudinal shift enables flexible control over the fundamental modes, whose frequency detuning can be reduced down to zero. Our coupled-mode theory analysis reveals an intrinsic link between the mode tuning and the transformation of slow-light dispersion at the photonic band-edge. We illustrate our approach through numerical modeling of cavities created in arrays of dielectric rods, and confirm our predictions with experimental observations.