Shape changes in [sup 79]Kr

High-spin states in [sup 79]Kr were studied using the [sup 65]Cu([sup 18]O,[ital p]3[ital n]) reaction at 65 MeV at the Florida State University Tandem-LINAC facility. Prompt [gamma]-[gamma] coincidences were observed using the Pitt-FSU detector array. Twelve new states were found, along with 19 new transitions. The yrast positive- and negative-parity bands were extended up to spins of (45/2[sup +]) and (31/2[sup [minus]]), respectively. Spin assignments were made based on directional correlation of oriented nuclei ratios whenever possible. A cranked-shell-model analysis shows some indication for a second band crossing in the positive-parity band at [h bar][omega][approx]0.75 MeV. This crossing, probably due to an aligned [ital g][sub 9/2] neutron pair, occurs with a much larger band interaction than the first [ital g][sub 9/2] proton crossing. An increase in signature splitting above [h bar][omega][approx]0.75 MeV and a return of large alternations in the [ital B]([ital M]1)/[ital B]([ital E]2) ratio is consistent with the theoretically predicted return to a nearly oblate shape.