Abstract: Pipe insulation sleeve and adhesive construction therefor, having a reduced amount of stress applied to the adhesive. A flexible foamed elastomeric tubular pipe insulation sleeve has a longitudinally extending slit which enables the sleeve or jacket to be placed around a pipe or portion thereof. An adhesive is applied to opposite walls of the slit, forming an adhesive joint, in order to hold the construction together after the insulation sleeve has been placed around a section of pipe. Stress on the adhesive joint is minimized or reduced in either of two ways. First, the tubular sleeve is formed with a V-shaped slit in which the opposite faces or walls of the slits intersect at an acute angle. In a preferred embodiment, the V is inverted (i.e., the open end of the V faces inwardly) and formed essentially along the minor axis of the elliptical shape which the sleeve assumes over time.