High-spin states of a number of nuclei near Ni-56 have been studied by means of the Si-28(Ar-36,x alpha ypzn) reaction. The GAMMASPHERE array in conjunction with light charged particle and neutron detectors were used to identify and cleanly select the fusion-evaporation products. In addition to significantly extending the level schemes of many previously known N = Z nuclei from Fe-52 to Cu-58, excited states in the one-neutron-hole nucleus Ni-55 and high-spin rotational bands in the vicinity of the doubly-magic Ni-56 have been established for the first time. Spherical-fp shell model and cranked Hartree-Fock calculations employing several Skyrme-type effective interactions have been used to interpret these data. The calculated moments of inertia of the rotational bands show considerable sensitivity to the details of the effective interactions.