We solve a correlated single-impurity Hamiltonian, developed from a model for the copper oxides. It consists of the Anderson or Wolff Hamiltonian supplemented by finite-range interactions. These couple the impurity to additional screening channels of conduction electrons in a way that allows low-energy fluctuations of both spin and charge. We use Wilson's numerical renormalization-group technique supplemented by analytic results to show that as the screening interactions increase, the effective repulsion at the impurity site changes to attraction. In the particle-hole symmetric model studied here, the low-energy properties then change from a spin Kondo effect to a charge Kondo effect in which the impurity fluctuates between zero occupation and double occupation. As the screening interactions are further increased, this Kondo-effect-Fermi-liquid ground state gives way to a critical line of non-Fermi-liquid states, through a Kosterlitz-Thouless-type transition. © 1994 The American Physical Society.