The structure of the odd-A isotopes 193,195,197 Pt, which lie along the line of stability, has been studied up to high spin through multi-nucleon transfer reactions. Positive-and negative-parity sequences in 193,195 Pt have been considerably extended and multiple band crossings established.An isomer with T 1/2 = 5.0(5) ns and I π = 25/2 − is present in 195 Pt. The isotopes 193,195 Pt are characterized by moderate oblate deformation, and angular momentum generation at high spin in the yrast, positive-parity sequences is attributed to the rotation alignment of i 13/2 neutrons and h 11/2 protons. A detailed understanding of the observed features is presented using calculations based on tilted axis cranking covariant density functional theory as well as others with the Ultimate Cranker code.