The invention relates to a roll-up strip (100) of labels (10, 10') that can be separated by a transverse cut of the strip, distinguishing on each label a main portion (2) from at least one of the longitudinal opposite ends (21, 22) of which there extends a longitudinal extension (3) of a smaller width than that of the main portion (2) and which distal end (31) defines a joining area (A) intended to be attached to a bag by external application of an accessory pressing element, the strip being able to be devoid of any reinforcement or filler made of plastic material, and a longitudinal cut or slit (6) being made in each joining area (A) of the labels of the strip, said cut or slit defining two portions (61, 62) therein, the purpose of which is to reduce the resistance offered by the said joining area to a deformation by transverse constriction to which it will be subject when the accessory pressing element is applied to it from the outside in the bag closing operation.