Single crystals of CeCu2Si2 were grown from metal solvents and their magnetic properties were systematically varied by partial substitution of Cu by Sn or In. The susceptibility χ is anisotropic and at high temperatures it is dominated by the crystal field split 4f state. At low temperatures the magnetic moments are drastically reduced. This reduction, as well as the Curie-Weiss temperature, depend sensitively upon the chemical composition. The observed variations both in the magnetic and the resistance behavior point to a Kondo-like coupling between local moments and conduction electrons. The strength of this interaction varies as the Fermi level is shifted by chemical means.