Thin-wall YBCO single-domain bulk materials present merits of reduced oxygen diffusion paths and large specific areas suitable for a fast oxygenation and a good thermal exchange. The progressive oxygenation under high pressure has been proposed to rapidly produce crack-free superconductors with stimulated trapping properties owing to speeding up of the oxygen diffusion. Thin-wall YBCO single domains grown by using top-seeded melt growth process were successfully oxygenated by applying this annealing treatment. Under oxygen pressure of 10 MPa, the influence of the dwell time and temperature on trapping properties was investigated. The trapped field was found to increase with up to 12 h and reach an optimum at . A 700 mT trapped field has been obtained on a large thin-wall single domain (46 mm in diameter) classically oxygenated, while waiting the delivery of a suitable high oxygen pressure furnace for such size.