The high-spin structure of the Xe-135 isotope was studied via prompt gamma-ray spectroscopy in two different experiments: (i) as a fission fragment following the fission of the Th-226 compound nucleus formed in a fusion-fission reaction and (ii) as an evaporation residue in the Xe-136(n,2n gamma)Xe-135 reaction. The level scheme above the previously known 11/2(-) isomer was established up to 3170-keV excitation energy. A strong sequence has been firmly assigned to Xe-135 and forms the yrast decay path including the (15/2(-)) and (19/2(-)) states. A much weaker sequence of gamma rays has been observed and tentatively assigned to Xe-135 and is a candidate for the off-yrast sequence that includes the (13/2(-)) and (17/2(-)) states, expected in the weak coupling of the h(11/2) neutron to the even-A core. The experimental results are compared with predictions from shell-model calculations.