A detailed study is presented of the instability of an initially motionless, ice-free and homogeneous layer of salt water which is sufficiently cooled from above such that ice formation occurs. Basic state boundary layer profiles of temperature and salinity are computed by solving the corresponding Stefan problem numerically. At sufficiently large Rayleigh numbers, these profiles become unstable to both direct and double diffusive instabilities. Of fundamental interest is the occurrence of a new type of oscillatory instability which is present when both temperature and salinity fields are destabilizing. Fastest growing modes are presented for the ice-water system. It is found that the wavelength of the dominant mode of convection increases with increasing ice thickness.