A multiple layer wraparound sleeve having a heat shrinkable backing layer and at least one functional layer has the functional layer as a discrete sheet which is connected to one end of the backing layer, and is of at least sufficient length that, when the sleeve is wrapped around the pipe or other substrate at least twice, the functional layer sheet wraps around the substrate first with its ends overlapping and the backing layer wraps around the functional layer sheet with its ends overlapping. This allows wrappings of reduced thickness to be employed without problems of voids occurring between the functional layer and the substrate.