The formation of large-scale structure is independent of the nature of the cold dark matter (CDM), however the fate of very small-scale inhomogeneities depends on the microphysics of the CDM particles. We investigate the matter power spectrum for scales that enter the Hubble radius well before matter–radiation equality, and follow its evolution until the time when the first inhomogeneities become non-linear. Our focus lies on weakly interacting massive particles (WIMPs), and as a concrete example we analyse the case when the lightest supersymmetric particle is a bino. We show that collisional damping and free-streaming of WIMPs lead to a matter power spectrum with a sharp cut-off at about 10−6 M⊙ and a maximum close to that cut-off. We also calculate the transfer function for the growth of the inhomogeneities in the linear regime. These three effects (collisional damping, free-streaming and gravitational growth) are combined to provide a WMAP normalized primordial CDM power spectrum, which could serve as an input for high-resolution CDM simulations. The smallest inhomogeneities typically enter the non-linear regime at a redshift of about 60.