The electrostatic ion cyclotron (EIC) and ion acoustic (IA) waves can be driven unstable by an electron current. The critical drift velocity of the electrons, at which the wave modes become unstable, depends on the parallel and perpendicular temperatures of the electrons and ions, and on the ion mass. We show that in plasma simulations the critical drift velocity for the electrostatic ion cyclotron wave has an additional dependence on the plasma magnetization, &OHgr;e/&ohgr;pe. This is negligible for naturally occurring ions, but becomes increasingly important when ion mass mi is reduced below the proton mass (mp=1836me). We have solved numerically the dispersion equation for the critically unstable EIC and IA waves for ion to electron mass ratios 40≤mi/me≤1836, and show how the reduction of the mass ratio affects the critical drifts. The temporal and spatial growth rates of the excited waves and changes in the wave behavior when the ion mass is reduced are discussed. It is shown that a careful selection of the ion to electron mass ratio has important consequences with regard to the interpretation of results of two-dimensional numerical simulations of electrostatic wave instabilities, since in certain parameter regimes the EIC wave behavior is strongly altered below a magnetization-dependent ion to electron mass ratio. ¿ American Geophysical Union 1994