This paper reports on the ground state nuclear moments measured in Cu58-62 using collinear laser spectroscopy at the ISOLDE facility. The quadrupole moments for Cu58-60 have been measured for the first time as Q (Cu-58) = 15(3) efm(2), Q (Cu-59) = -19.3(19) efm(2), Q(Cu-60) = +11.6(12) efm(2) and with higher precision for Cu-61.62 as Q (Cu-61) = -21.1(10) efm(2), Q(Cu-62) = -2.2(4) efm(2). The magnetic moments of Cu-58.59 are measured with a higher precision as(IL)(Cu-58) = +0.570(2)(ILN) and (IL)(Cu-59) = +1.8910(9)(ILN). The experimental nuclear moments are compared to large-scale shell-model calculations with the GXPF1 and GXPF1A effective interactions, allowing the softness of the Ni-56 core to be studied. (C) 2011 Published by Elsevier B.V.