Abstract. We examine how the growth of magnetospheric whistler-mode waves depends on the cold (background) electron number density N₀. The analysis is carried out by varying the cold-plasma parameter a = (electron gyrofrequency)²/(electron plasma frequency)² which is proportional to 1/N₀. For given values of the thermal anisotropy A_T and the ratio N_h/N₀, where N_h is the hot (energetic) electron number density, we find that, as N₀ decreases, the maximum values of the linear and nonlinear growth rates decrease and the threshold wave amplitude for nonlinear growth increases. Generally, as N₀ decreases, the region of (N_h/N₀, A_T)-parameter space in which nonlinear wave growth can occur becomes more limited; that is, as N₀ decreases, the parameter region permitting nonlinear wave growth shifts to the top right of (N_h/N₀, A_T) space characterized by larger N_h/N₀ 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.