The dependence of the far infrared Josephson photoresponse of current biased granular high‐Tc superconductor thin films on deoxygenation is presented. Bi2Sr2CaCu2O8 and TlBa2Ca2Cu3O9 thin films were heated in vacuum to temperatures of between 200 and 500 °C. The resulting deoxygenation weakens the intergrain coupling, thereby reducing the critical current and enhancing the photoresponse. In this way the optimum temperature for the fast Josephson response may be tuned to lie outside the temperature region of the slow bolometric signal.