The problem of steady convection rolls and their instabilities in a fluid layer heated from below is studied numerically in the case of a highly conducting, rigid lower and a nearly insulating, stress‐free upper boundary. A Galerkin method is used to obtain two‐dimensional solutions in dependence on the Rayleigh numberRand the wave number &agr; for different values of the Prandtl numberP. Their stability is analyzed through the superposition of general three‐dimensional infinitesimal disturbances. Most instabilities correspond qualitatively to those found in the case of symmetric highly conducting, rigid boundaries. A new instability, the subharmonic varicose instability, is found, however, which restricts the region of stable rolls toward a higher Rayleigh number in the case of moderate Prandtl numbers. ©1995 American Institute of Physics.