We study the transmission of diffuse light through thick slits. For perfectly conducting slits and in-plane s-polarized illumination, the transmittance curves present a staircaselike behavior as a function of the aperture width, where the steps mark the appearance of new propagation modes. In contrast, with p-polarized illumination the transmittance increases linearly with the aperture width, with only some perturbations in the positions that correspond to the appearance of new modes. Out-of-plane incidence and more realistic assumptions about the slit, such as finite conductivity and roughness, are also discussed.