The invention relates to a method for pressing together empty containers, especially drinks bottles or cans made of plastic, especially PET or tinplate, comprising a housing (1) with a fill opening (2) and an outlet (3), in addition to a cutting and pressing unit (4) disposed in said housing, and means for driving and controlling the cutting and pressing unit (4). The cutting and pressing unit (4) contains at least two rollers (4.1 and 4.2) whose axes of rotation are arranged at a distance from each other. Each roller (4.1 and 4.2), when seen in the longitudinal direction of the axis of rotation (A1; A2) thereof, comprises at least two, preferably several sections (S1 and S2). Sections (S1 and S2) successively following each other in an alternate manner respectively have another diameter (D1; D2). When the two rollers (4.1 and 4.2) are mounted, at least the sections (S2) having the larger diameter are arranged in such a way that they are offset in relation to each other and the peripheral surfaces thereof partially overlap with each other, forming cutting disks (5) whose peripheral surfaces are respectively provided with at least one groove.