We report on observations obtained with the adaptive optics system at the 10 m Keck II Telescope during engineering validation and early science observing time for the adaptive optics system. We observed Neptune at near-infrared wavelengths. Angular resolution was 0.05"-0.06", corresponding to a spatial scale of approximately 1000 km at Neptune. We discuss the latitudinal structure of circumferential cloud bands and of compact infrared-bright features seen in the southern hemisphere, as well as their variation with wavelength. We determine the values of I/F (proportional to the ratio of reflected intensity to incident solar flux) in the J and H infrared-wavelength bands, including narrowband filters where there is strong methane absorption. We use the I/F values inside and outside of methane bands to estimate the altitude of clouds responsible for the brightest compact features in the infrared. Our data show that, on two of our four observing dates, the brightest region on Neptune contained highly reflective haze layers located below the tropopause but not deeper than a few bars.