Abstract : This article reports on the ground-state spin and moments measured in 72,74Cu using collinear laser spectroscopy at the CERN On-Line Isotope Mass Separator (ISOLDE) facility. From the measured hyperfine coefficients, the nuclear observables μ(72Cu)=-1.3472(10)μN, μ(74Cu)=-1.068(3)μN, Q(72Cu)=+8(2) efm2, Q(74Cu)=+26(3) efm2, I(72Cu)=2, and I(74Cu)=2 have been determined. Through a comparison of the measured magnetic moments with different models, the negative moment reveals a strong πf5/2⊗νg9/2 component in the ground-state wave function. Consequently, a negative parity has been assigned to the ground states of 72,74Cu. Large-scale shell-model calculations illustrate the strong sensitivity of the nuclear moments to configuration mixing and to the effective interaction employed.