A system for preparing beverages comprising a cartridge containing a supply support of multiple individual portions provided so that can be operated by a beverage preparation machine, the supply support including support sheets juxtaposed and united to each other along a connection plane wherein the beverage preparation machine comprises an extraction device configured so that can retain the collection portions around collection confinements, each collection confinement presenting a total height that extends on both sides of the connection plane, and each collection confinements presenting a characteristic transversal collection dimension in the connection plain, and, wherein ratio between the characteristic transversal collection dimension and the total height that extends on both sides of the connection plane of between 3.0:1 and 6.0:1.