Two excited well-deformed bands have been observed in the semi-magic nucleus Ni-58. One of the bands was observed to partially decay by emission of a prompt discrete alpha particle that feeds the 2949 keV 6(+) spherical yrast state in the daughter nucleus Fe-54. This constitutes the first observation of prompt alpha emission from states lying in the deformed secondary minimum of the nuclear potential. gamma -ray linking transitions via several parallel paths establish the spin. parity, and excitation energy of this deformed band in Ni-58
