The medium-spin structure of the nuclei 93 Rb and 95 Rb is studied following the neutron-induced fission of 235 U at the PF1B neutron guide, using the FIFI spectrometer, and at the Lohengrin mass spectrometer of the Institut Laue-Langevin Grenoble. These nuclei, plus 91 Rb, are also studied following the spontaneous fission of 248 Cm and 252 Cf sources, using the EUROGAM-II and Gammasphere detector arrays, respectively. A high-spin isomeric state, with a half-life of 111(11) ns, is found in 93 Rb at an excitation energy of 4422.4 keV, which most likely corresponds to the fully aligned [π (g 9/2 ) ⊗ ν(g 7/2 h 11/2 )] 27/2 − configuration. An analogous configuration is proposed for the 5297.9-keV level observed in 91 Rb. A new E3 decay branch of the 1133.9-keV isomer in 91 Rb is found, for which the rather low transition rate of B(E3) = 3.8(10) W.u. is determined. The energy of the isomeric state of 95 Rb is now proposed to be at 810.6 keV, with a spin of (9/2 + ), and its half-life determined to be T 1/2 = 94(7) ns. A cascade of prompt transitions is observed on top of the 810.6-keV isomer in 95 Rb. The near-yrast structures of 91 Rb, 93 Rb, and 95 Rb are compared to the results of shell-model calculations, which support the proposed 27/2 − interpretation of states in 91 Rb and 93 Rb. An analogous 27/2 − state is expected to occur in 95 Rb, as a long-lived isomer at 3.24 MeV. No such isomeric decay could be observed in a measurement using the Lohengrin spectrometer, which shows that, if it exists, its population, following the fission of 235 U, is at least four times lower than that of the analogous 27/2 − isomer in 97 Y.