[en] High-spin states in the odd-proton nuclei ^119,121,123I and ^121,127,131Cs are studied following heavy-ion fusion-evaporation reactions using beams provided by the Stony Brook Tandem-LINAC accelerator. Gamma-rays resulting from deexcitations of high-spin states are measured using an array of six Compon-suppressed germanium detectors. Experiments performed include excitation functions, angular distributions, γ-γ coincidence and pulsed-beam E_γ-t measurements. Following theoretical predictions of competing prolate and oblate potential-energy minima, experimental evidence is presented for the coexistence of prolate and oblate nuclear shapes in ^119,121,123I. Both prolate and oblate rotational bands are observed with the same single-quasiproton configuration in each nucleus. Rotational bands in the Z = 55 Cs isotopes are found to be prolate at low spins. At higher spins, these nuclei possesses different shapes ranging from prolate to oblate, depending on the neutron number N. These shape differences result from the alignment of an h_11/2 neutron pair. The systematic behavior of neutron alignment is investigated. The change in the signature splitting and B(M1)/b(E2) ratios for bands below and above the alignment indicates that the shape changes are consistent with the γ-driving properties of h_11/2 neutrons. Finally, non-collective states are observed to become yrast at moderate spins in ¹¹⁹I and ¹²¹I