High-spin states in Kr-77 were identified via analysis of prompt gamma-gamma coincidences in the Ni-58(Si-29,2 alpha 2p) reaction at 128 MeV at the Gammasphere facility. Evaporation channel selection was achieved using the 95 element Microball charged-particle detector. 27 new states and 42 new transitions were found, The positive-parity bands were confirmed and the alpha=-1/2 band extended to 39/2(+). The negative-parity signature pair was extended to 31/2(-) and 37/2(-). Two new high-lying negative-parity bands were found extending from a state of spin I = 15/2 and energy 2.6 MeV to 17.4 MeV at I = (55/2). The new bands appear highly deformed and become yrast at high spin. A three-quasiparticle structure based on deformation driving, low-K unique-parity and intruder orbitals is suggested for them.