A new closed-form relation for the elastic compliance of a film-substrate system indented by a flat cylindrical punch is presented. The relation is an extension of the work of Gao at al.  modified to increase the applicable range of modulus mismatch between the film and substrate. The accuracy of the relation is assessed by comparison to finite element simulations, other approximate numerical solutions, and nanoindentation experiments performed on a fluorinated silicate glass (FSG) film on a silicon substrate. The benefits and limitations of the relation are discussed.