Assembly for opening cigarette wrappers in a machine for recovering tobacco from defective and/or substandard cigarettes in which the cigarettes are translated to be cut along guiding grooves and at least one revolving disc knife is provided above each cigarette, each axis of rotation on which a disc knife is mounted lying on a plane parallel to the plane over which the cigarette axes move, characterized in that the plane of at least one disc knife does not comprise the axis of the cigarette and is parallel to the said axis and in that the assembly is provided with means for blocking the possibility of rotation of the cigarettes around their axes in the guiding grooves.