A device for applying compression treatment to a part of a wearer's body comprises first and second inflatable bladders spaced apart from one another along an axis of the device. A line of weakness in a connecting section between the first and second bladders extends generally transverse to the axis of the device for selectively separating the inflatable bladders from one another. The device includes an overlying layer in generally opposing relationship to one of the first and second bladder layers. The overlying layer is discontinuous generally adjacent to the line of weakness to define terminal edge margins of the overlying layer extending generally along the line of weakness. Each of the terminal edge margins are connected to at least one of the first and second bladder layers on an opposite side of the line of weakness from the other terminal edge margin.