We show that the methane bands in Titan's spectrum are saturated and that, consequently, either the methane abundance is nearly an order of magnitude greater than is generally believed or else methane is a minor constituent in this atmosphere. Consideration of the physical constraints for Titan's atmosphere leads to a model which describes the bulk composition in terms of observable parameters. Intermediate-resolution photometric scans of both Saturn and Titan, including our scans of the Q-branch of Titan's 3V3 methane band, constrain these parameters in such a way that the model indicates the presence of another important atmospheric gas, namely, another bulk constituent or a significant thermal opacity. The simplest interpretations of the published observations are not all compatible; further progress in determining the composition and state of Titan's atmosphere requires additional observations to eliminate the present ambiguities. For this purpose we suggest particular observational targets.