The determination of both the optical constants and thickness of thin, optically absorbing films, particularly on opaque substrates, is a difficult problem when approached solely with ellipsometric techniques. This is due to the strong statistical correlation which exists between the optical constants of the film (primarily the extinction coefficient) and the thickness of the film when adjusting these parameters to fit the experimental ellipsometric data. In this paper we present several techniques which are useful for the solution of this problem, and illustrate the success of these individual techniques with analysis of several thin films of amorphous hydrogenated carbon.