Abstract: Pieces of meat are tumbled with a marinade in a tumbler that has a smoothly continuous surrounding side wall with no protrusions or baffles or other protrusions contacting the pieces of meat. The tumbler is rotated about the axis of the side wall and gas is pumped from the tumbler during the tumbling to maintain a reduced pressure. The gas may be pumped to maintain a lower reduced pressure for a first time interval and to permit a higher pressure, still below atmospheric pressure, for a second period of time during a rest period. These two pressure levels are alternated during the alternate tumbling and rest periods.