Abstract. We examine how the growth of magnetospheric whistler-mode waves depends on the cold (background) electron number density N 0 . The analysis is carried out by varying the cold-plasma parameter a = (electron gyrofrequency) 2 /(electron plasma frequency) 2 which is proportional to 1/N 0 . For given values of the thermal anisotropy A T and the ratio N h /N 0 , where N h is the hot (energetic) electron number density, we find that, as N 0 decreases, the maximum values of the linear and nonlinear growth rates decrease and the threshold wave amplitude for nonlinear growth increases. Generally, as N 0 decreases, the region of (N h /N 0 , A T )-parameter space in which nonlinear wave growth can occur becomes more limited; that is, as N 0 decreases, the parameter region permitting nonlinear wave growth shifts to the top right of (N h /N 0 , A T ) space characterized by larger N h /N 0 values and larger A T values. The results have implications for choosing input parameters for full-scale particle simulations and also in the analysis of whistler-mode chorus data.