Multi-quasiparticle high-K states in neutron-deficient mercury, lead, and polonium isotopes have been investigated systematically by means of configuration-constrained potential-energy-surfacecalculations. An abundance of high-K states is predicted with both prolate and oblate shapes, which extends the shape coexistence of the mass region. Well-deformed shapes provide good conditions for the formation of isomers, as exemplified in 188 Pb. Of particular interest is the prediction of low-lying 10 − states in polonium isotopes, which indicate long-lived isomers.