The first detailed comparison between predictions of theories for detonatios are presented here. Provided the unperturbed Z-N-D profile only exhibits instability at long transverse wavelengths with a simple stability diagram, the computed regular cell spacing is found to agree remarkably well with simple theories based on the most unstable linearized wavelengths when the channel width is not too large. Neither the geometric acoustic theories nor theories based upon a linearized unstable wavelength provide an accurate prediction of the computed cell-spacing for Z-N-D profiles with a complex stability diagram such as those that are unstable at short transverse wavelengths. Several new features of detonation instability are also documented here through the numerical simulations, including regimes exhibiting the transition to fully developed turbulence in the wake of the unstable detonation front as the activation energy and heat release are increased. Furthermore, the computations indicate that this strong turbulence contributes to the irregularity of the cellular pattern.