The invention relates to a process for producing respirable air comprising the following stages: treatment of compressed air comprising an air-drying operation; and rehumidification of the treated dry air. According to the invention, the rehumidification stage of the treated dry air comprises an operation of controlled distribution of the treated dry air on the one hand in a rehumidification line (24), and on the other hand in a dry line (22). The invention also relates to an installation (1) for utilising such a process. Application to the area of nuclear installation dismantling.