The reasons for cracking of YBa2Cu3Oδ/Y2BaCuO5 (Y123/Y211 or YBCO) bulk single-grain superconductors are mechanical stresses, which arise in the sample during its fabrication. Two main sources of stresses appearing during fabrication were identified: the different thermal expansion coefficients of 123 and 211 phases and the dependence of 123 phase lattice parameters on the oxygen stoichiometry. As-grown YBCO bulks have low oxygen content, YBa2Cu3O6.3, are not superconducting, and must be oxygenated to form YBa2Cu3O7. During standard oxygenation at 400 °C the shortening of crystal lattice parameters causes intensive cracking. The created cracks allow oxygen penetration into the bulk and cause the oxygenation time to be technologically acceptable but reduce significantly the superconducting properties. Here we show that it is possible to eliminate the formation of oxygenation cracks and to reach a critical current density 2.5 times higher than in material bulk oxygenated in a standard way. The oxygenated crack-free samples were obtained by high pressure oxygenation with progressively increasing oxygen partial pressure.