Modification of the Zeeman splitting of conduction-electron spins by an s–d exchange interaction has been studied in the de Haas – van Alphen effect at fields up to 50 kG and temperatures of order 1 K in very dilute copper-based alloys of Cr, Mn, Fe, and Co. In Cu(Cr) there is a linear relationship between an effective exchange energy and solute concentration, and the results indicate an antiferromagnetic interaction between conduction electrons and polarized impurity spins with very little Kondo screening. The effects of increasing field or decreasing temperature are consistent with a simple polarization of the impurity spins. The variation of the exchange energy from orbit to orbit is explained by the variation over the copper Fermi surface of the d-like part of the wave function. The occurrence of clean spin-splitting zeros in the Cu(Cr) system is believed to be a fortuitous result of a symmetrical positioning of the Friedel virtual bound states relative to the Fermi energy. In Cu(Mn) the exchange energy effects are similar to those in Cu(Cr) but involve also a differential scattering of the two spin components in the de Haas – van Alphen oscillations which results in spin-splitting minima rather than zeros. In Cu(Fe) and Cu(Co) differential scattering effects are also observed, but in Cu(Fe) the exchange energy is markedly reduced and in Cu(Co) it is almost completely eliminated by spin compensation of the impurity moment by conduction electrons.