With my collaborators (Ivan Hubeny, NASA/Goddard Space Flight Center; Marcos Diaz, Catherine Grant, and Darren Williams, all of Penn State), I am computing the structure of discs and their corresponding UV spectra for a large grid of choices of the white dwarf mass Mwd and the mass transfer rate Ṁ. In our approach, we divide the problem into a number of parts, each corresponding to a particular FORTRAN-implemented computer program. Program TLUSDISK computes the vertical structure for individual rings in the disc (T, ρ, ne, τ versus Z). The rings are treated independently, as plane-parallel entities without irradiation, obeying the standard expression for Teff as a function of Mwd, Rwd and Ṁ. With this vertical structure, program SYNSPEC computes the detailed local (rest frame) spectrum for each ring. Both specific intensities and angle-averaged fluxes can be computed. Program DISKSYN is used to combine the spectra of individual rings to obtain the integrated or whole-disc spectrum, taking into account Doppler shifts (dependent on the chosen disc inclination) and limb darkening. Finally, program ROTINS is used to smooth the spectrum to an appropriate instrumental resolution. Intermediate results, e.g., from TLUSDISK or SYNSPEC, are stored for repeated use.