We investigate current fluctuations in nondegenerate semiconductors, on length scales intermediate between the elastic and inelastic mean free paths. We present an exact solution of the nonlinear kinetic equations in the regime of space-charge limited conduction, without resorting to the drift approximation of previous work. By including the effects of a finite voltage and carrier density in the contact region, a quantitative agreement is obtained with Monte Carlo simulations by González et al., for a model of an energy-independent elastic scattering rate. The shot-noise power P is suppressed below the Poisson value PPoisson=2eĪ (at mean current Ī) by the Coulomb repulsion of the carriers. The exact suppression factor is close to 1/3 in a three-dimensional system, in agreement with the simulations and with the drift approximation. Including an energy dependence of the scattering rate has a small effect on the suppression factor for the case of short-range scattering by uncharged impurities or quasielastic scattering by acoustic phonons. Long-range scattering by charged impurities remains an open problem.