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The high-spin structures and isomers of the N = 81 isotones 135 Xe and 137 Ba are investigated after multinucleon-transfer (MNT) and fusion-evaporation reactions. Both nuclei are populated (i) in 136 Xe+ 238 U and (ii) 136 Xe+ 208 Pb MNT reactions employing the high-resolution Advanced Gamma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA, (iii), in the 136 Xe+ 198 Pt MNT reaction employing the γ-ray array GAMMASPHERE in combination with the gas-detector array CHICO, and (iv) via a 11 B+ 130 Te fusion-evaporation reaction with the HORUS γ-ray array at the University of Cologne. The high-spin level schemes of 135 Xe and 137 Ba are considerably extended to higher energies. The 2058-keV (19/2 − ) state in 135 Xe is identified as an isomer, closing a gap in the systematics along the N = 81 isotones. Its half-life is measured to be 9.0(9) ns, corresponding to a reduced transition probability of B(E2, 19/2 − → 15/2 − ) = 0.52(6) W.u. The experimentally-deduced reduced transition probabilities of the isomeric states are compared to shell-model predictions. Latest shell-model calculations reproduce the experimental findings generally well and provide guidance to the interpretation of the new levels.