The short-time kinetic equation for hard spheres derived by Lebowitz, Perçus, and Sykes is compared with the Enskog equation. It is shown that, to leading order in the density, the short-time equation and the Enskog equation are identical and equivalent to the memory function equation used by Mazenko, Wei, and Yip. By using simple properties of the collision integrals, the scattering function calculated from the short-time equation can be related to the scattering function obtained from the Enskog equation: This relationship is exact for all values of the density. We examine the relationship in the short-time limit and in the hydrodynamic limit and argue that the short-time kinetic equation gives a better description of the scattering function than does the Enskog equation...