  We report on calculations of the translational and rotational short-time
self-diffusion coefficients $D^t_s$ and $D^r_s$ for suspensions of
charge-stabilized colloidal spheres. These diffusion coefficients are affected
by electrostatic forces and many-body hydrodynamic interactions (HI). Our
computations account for both two-body and three-body HI. For strongly charged
particles, we predict interesting nonlinear scaling relations $D^t_s\propto
1-a_t\phi^{4/3}$ and $D^r_s\propto 1-a_r\phi^2$ depending on volume fraction
$\phi$, with essentially charge-independent parameters $a_t$ and $a_r$. These
scaling relations are strikingly different from the corresponding results for
hard spheres. Our numerical results can be explained using a model of effective
hard spheres. Moreover, we perceptibly improve the known result for $D^t_s$ of
hard sphere suspensions.
