Decay paths, half-lives, and excitation energies of the i13/2 bandheads of the neutron-deficient nuclei 171Pt, 167Os, and 163W have been established for the first time. Gamma-ray transitions, X-rays, and internal conversion electrons have been observed, allowing internal-conversion coefficients to be measured and B(M2) reduced transition probabilities to be extracted. These results elucidate the low-lying single-quasiparticle structures and give the energy level spacings between the νf7/2, νh9/2, and νi13/2 quasineutron states for all three nuclei. Moreover, ground-state spin assignments have been made for the first time, along with the measurement of the α-decay branching ratio for 171Pt. The decay paths of the i13/2 bandheads were followed by favored α decays, indicating that all three nuclei have the same Iπ=7/2− ground state.