Abstract: The high-spin structures of Ba-136 and Ba-137 are investigated after multinucleon-transfer (MNT) and fusion-evaporation reactions. Ba-136 is populated in a Xe-136 + U-238 MNT reaction employing the high-resolution Advanced GAmma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA at the Laboratori Nazionali di Legnaro, Italy, and in two Be-9 + Te-130 fusion-evaporation reactions using the High-efficiency Observatory for gamma-Ray Unique Spectroscopy (HORUS) at the FN tandem accelerator of the University of Cologne, Germany. Furthermore, both isotopes are populated in an elusive reaction channel in the B-11 + Te-130 fusion-evaporation reaction utilizing the HORUS gamma-ray array. The level scheme above the J(pi) = 10(+) isomer in Ba-136 is revised and extended up to an excitation energy of approximately 5.5 MeV. From the results of angular-correlation measurements, the E-x = 3707- and E-x = 4920-keV states are identified as the bandheads of positive- and negative-parity cascades. While the high-spin regimes of both Te-132 and Xe-134 are characterized by high-energy 12(+) -> 10(+) transitions, the Ba-136 E2 ground-state band is interrupted by negative-parity states only a few hundred keV above the J(pi) = 10(+) isomer. Furthermore, spins are established for several hitherto unassigned high-spin states in Ba-137. The new results close a gap along the high-spin structure of N < 82 Ba isotopes. Experimental results are compared to large-scale shell-model calculations employing the GCN50:82, Realistic SM, PQM130, and SN100PN interactions. The calculations suggest that the bandheads of the positive-parity bands in both isotopes are predominantly of proton character.