Area scanner measurements of the brightness distributions of Uranus at 6300 and 7250 Å are presented. At the former wavelength, which is characteristic of continuum radiation, the observed limb-darkening is consistent with the results of Stratoscope observations. At the latter wavelength, in the center of a strong methane absorption band, the planet shows substantial limb-brightening as has been reported by other investigators. The limb-brightening and geometric albedo of Uranus in this methane band can be explained in terms of a clear atmospheric model in which the methane partial pressure above the saturation level is equal to its equilibrium vapor pressure. This conclusion is relatively insensitive to the methane mixing ratio below the saturation level. The presence of a high-altitude, conservatively, isotropically scattering haze of optical thickness 0.1, such as that previously proposed as a possible cause of the 7250-Å limb-brightening, would produce a geometric albedo at this wavelength that is substantially larger than the value observed for Uranus.