Abstract: A apparatus and a method for applying pressure to a human body, the apparatus comprising a compression sleeve with a plurality of inflatable annular cells, a control block with pneumatic valves, and a pressurized fluid source. The most distal cell of the sleeve is designated by number 1, while the most proximal cell is designated by number N. The control block is adapted to perform a regular therapy procedure starting by inflation of the most distal cell or group of cells, and a pre-therapy procedure, preceding the regular therapy procedure, including a succession of cell inflation-deflation subcycles. Each subcycle is performed at least once over a range of at least two adjacent cells, starting with an initial cell different from cell N, progressing towards and ending with cell N. The initial cell of the first subcycle is one of the most proximal one-third of cells, and the initial cell of each next subcycle has a number monotonously and gradually approaching 1.