The perturbative hypernetted-chain (PHNC) equation developed recently has been applied to the one-component plasma (OCP) and the one-component charged hard-sphere (OCCHS) systems in a uniform compensating background. Computed thermodynamic properties and pair correlation functions show that the PHNC gives excellent agreement with computer simulations and that it is as accurate as (or, in some cases, superior to) the reference-hypernetted chain and the hypernetted-chain-mean spherical equations, representing the two best currently available theories. The PHNC also predicts the OCP screening function at short range in close agreement with computer simulations and is superior to other theoretical results. Reliability of the radial distribution function at the hard-sphere contact distance for the OCCHS is also discussed.