The positive-parity yrast states in the ⁸⁹Rb, ⁹²Y, and ⁹³Y nuclei were studied using gamma-ray spectroscopy with heavy-ion induced reactions. In the multinucleon transfer reactions ²⁰⁸Pb+⁹⁰Zr (590 MeV) and ²³⁸U+⁸²Se (505 MeV), several gamma-ray transitions were identified in these nuclei by means of coincidences between recoiling ions identified with the PRISMA spectrometer and gamma rays detected with the CLARA gamma-ray array in thin target experiments. Level schemes were subsequently determined from triple gamma coincidences recorded with the GASP array in a thick target experiment, in the reactions produced by a 470 MeV ⁸²Se beam with a ¹⁹²Os target. The observed level schemes are compared to shell-model calculations.