Gamma-ray transitions have been identified for the first time in the extremely neutron-deficient Tz = 1 nuclide 110Xe and the energies of the three lowest excited states in the ground-state band have been deduced. A level scheme has also been constructed for the proton-unbound, T z = 3/2 nuclide 109I, exhibiting band structures built on g7/2 and h11/2 states in a weakly deformed, triaxial nucleus. In addition, a third band is proposed to be built on a g7/2 orbital coupled to an octupole-vibrational phonon of the 108Te core. The results were obtained in a recoil-decay tagging experiment using the 58Ni(54Fe,2n/p2n) reaction at a beam energy of 195 MeV. The experiment was performed using the highly efficient JUROGAM γ-ray spectrometer in conjunction with the RITU gas-filled recoil separator and the GREAT focal-plane spectrometer. The results on 110Xe establish a breaking of the normal trend of increasing first excited 2+ and 4+ level energies as a function of decreasing neutron number as the N = 50 major shell gap is approached for the neutron-deficient Xe isotopes. This unusual feature is suggested to be an effect of enhanced collectivity, possibly arising from isoscalar n-p interactions becoming increasingly important close to the N = Z line. Features in the low-lying levels of 106Te and 109I, showing similar trends, are also discussed.