The surfaces of soft thin elastic films bonded to two rigid substrates become spontaneously rough due to the attractive intersurface interactions when the intersurface distance declines sufficiently to produce a critical force. The effects of compressibility on the conditions for surface roughening and its length scale are investigated. For highly compressible films (nu less than 0.25), surface roughening is not possible. The critical force required for the onset of instability and its wave number both decline with increased compressibility. The wavelength of the instability is influenced much more by the properties of the more compliant film [compliance equals (1-2nu)h/2mu(1-nu)]. There is an abrupt change in the wavelength as the compliances of the two films become nearly equal.