The optical losses in dry-etched monolithic microresonators have been studied as a function of their lateral dimensions. Cylindrical microresonators with various radii have been etched from a planar GaAlAs/GaAs microcavity with a very high quality factor (Q≅11 700). Measurements of the resonance linewidth, using Ti-sapphire laser spectroscopy allowed to study the degradation of the Q factor at small radii. The Q factor is four times smaller in 1.1 mum radius microresonators, compared to the unprocessed cavity. This degradation is attributed to optical scattering from sidewalls, whose efficiency is shown to scale with the guided mode intensity at the microresonator edge.