The thermally induced fluctuations in vertical displacement at the surface of a semi-infinite simple fluid are considered, and the wavevector and frequency dependences of their power spectrum are obtained. The fluid is assumed to have non-zero surface tension, viscosities, compressibility and thermal conductivity, and the theory generalizes previous work that neglected the last two attributes. It is found that the thermal conductivity has a small effect for normal values of the fluid parameters, in contrast to its important role in the central peak of the bulk spectrum. The non-zero compressibility leads, however, to additional continua in the surface spectrum that correspond to the displaced acoustic-wave peaks in the bulk spectrum. Numerical results for liquid argon and mercury are presented.