Zerodur and BK7 glass substrates (developed by Fa. Glaswerke Schott, D-55014 Mainz, Germany) from Carl Zeiss Oberkochen polished to a standard surface roughness of varsigma = 0.8 nm rms were coated with a C layer by electron-beam evaporation in the UHV. The roughness of the C-layer surfaces is reduced to 0.6 nm rms. A normal-incidence reflectance of 50% at a wavelength of 13 nm was measured for a Mo/Si multilayer soft-x-ray mirror with 30 double layers (N = 30) deposited onto the BK7/C substrate, whereas a similar Mo/Si multilayer (N = 30) evaporated directly onto the bare BK7 surface turned out to show a reflectance of only 42%.