Many functions have been proposed for estimating signal information content and complexity on the time-frequency plane, including moment-based measures such as the time-bandwidth product and the Shannon and Renyi entropies. When applied to a time-frequency representation from Cohen's class, the Renyi entropy conforms closely to the visually based notion of complexity that we use when inspecting time-frequency images. A detailed discussion reveals many of the desirable properties of the Renyi information measure for both deterministic and random signals.