Ag‐sheathed powder‐in‐tube wires on the basis of the highTcsuperconductor YBa2Cu3Oxare produced by a drawing process. After cold working, the wires are not superconducting. By heat treatment at temperatures >900 °C, lattice defects are healed and the contact between the grains is improved. After this heat treatment the wires are slowly cooled in an O2atmosphere in order to adjust the optimum O2stoichiometry. The annealing temperature has a strong influence on the attainable critical current density. By annealing a wire with 420 ppm carbon content at 950 °C,jcvalues of 5020 A/cm2at 4.2 K and 1130 A/cm2at 77 K were achieved. Drastically reduced critical current densities in wires with high carbon content demonstrate the importance of a low carbon content for achieving high critical current densities in YBa2Cu3Ox.