The ability to retrieve key information about clouds from observations of atmospheric absorption by molecular oxygen along with the O2-O2 collision complex is examined. Specifically, the fractional absorption of scattered solar radiation in the oxygen A and B bands and the 477 nm O2-O2 absorption band at moderate resolution (0.5--6.0 nm) is shown to allow estimates to be made not only of cloud optical depth but also of cloud base and top heights from a down-looking observing platform above cloud level. We first demonstrate through theoretical calculations that these cloud parameters can be accurately retrieved from measurements of fractional absorption at this moderate resolution and with no requirement of absolutely calibrated radiances. Further, it is shown that the addition of B band and O2-O2 absorption information to A band observations can decrease the uncertainty in these cloud parameter estimates by more than 50% (depending on the cloud's properties) compared to using A band information alone. The theoretical analysis is supported by sample, above-cloud measurements of the oxygen A band fractional absorption associated with hurricane Michelle over the Gulf of Mexico. The experimental results are in excellent agreement with the cloud base and top heights inferred from cloud photographs and from dropsonde relative humidity data, demonstrating the capability of this approach for improved cloud remote sensing.