The increasing use of high-temperature, high-pressure hydroprocessing has stimulated the need to minimize process unit turn-around time. Both the restreaming of active catalyst at turn-around and the discharging of spent catalyst must be preceded by a cooling of the vessel wall to ambient temperature. Consequently, temperature-time and pressure-time profiles must be selected which transform the unit from operating temperature and hydrogen pressure to ambient temperature and zero hydrogen pressure without : (1) generation of excessive thermal stress in vessel walls, (2) coke formation on catalyst, (3) overlay disbonding or (4) crack initiation and growth due to base-metal hydrogen embrittlement. This paper describes a method for selecting the temperature-time and pressure-time profiles which produce outgassing in minimum time consistent with these constraints. The outgassing time computed by this method for a particular unit is a theoretical minimum in the sense that a shorter time is not possible without violating one of the constraints; this procedure can therefore be used as a standard of reference against which other procedures can be compared. Conversely, the procedure is also practical and can be implemented on actual process units. Improved outgassing methods can result in significant cost savings by reducing equipment downtime. The U.S. Patent and Trademark Office has advised the authors that this outgassing procedure is patentable and that a patent will be issued in due course.