Rotary pressure distributor for a carousel-type hollow-body treatment machine, comprising several treatment stations, this distributor comprising two coaxial rings (2, 3) in sealed contact, one of them (3) a rotary ring comprising communication orifices (6) connected to at least one treatment station and the other (2) stationary and comprising several slots (7) connected to a pressure source of the machine, these orifices and slots being distributed over several concentric circumferences (9) of different diameters; the orifices and/or the slots positioned on the different diameters have anterior and posterior ends (11, 12) shaped in such a way that as the orifices slide past the respective slots, the rates at which the surface area of the passage (13) defined by each orifice and the associated slot increase upon opening and decrease upon closing are substantially the same over all the circumferences.