The isotopes Ni68-74, Of interest both for nuclear physics and astrophysics, have been produced in proton-induced fission of U-238 and ionized in a laser ion guide coupled to an on-line mass separator. Their beta decay was studied by means of beta-gamma and gamma-gamma spectroscopy. Half-lives have been determined and production cross sections extracted. A partial level scheme is presented for Cu-73 and additional levels for Cu-71, providing evidence for a sharply lowered position of the pi 1f(5/2) orbital as occupancy of the nu 1g(9/2) state increases. The latter may have a clear impact on the predicted structure and decay properties of doubly magic Ni-78. [S0031-9007(98)07340-2].