A transfer cylinder sleeve is provided for an offset printing machine including an inner carrier layer, a compressible layer and a covering layer, where at least one of the layers has a joint or a gap and provided that when a joint or a gap is used in the covering layer, then the transfer cylinder sleeve is applied to a transfer cylinder in register so that the joint in the covering layer rests opposite a tension channel of a plate cylinder during rolling contact of the transfer cylinder with the plate cylinder. Optionally, a non-stretchable layer is provided between the compressible layer and the covering layer, or alternatively, a non-stretchable material is provided in the compressible layer itself.