A woven sleeve for routing and protecting an elongate member and method of construction thereof are provided. The sleeve has a woven wall with a circumferentially continuous outer periphery extending along a central axis between opposite ends. Warp yarns extend generally parallel to the central axis and fill yarns extend generally transversely to the warp yarns. At least a portion of the wall has a plurality of layers in abutment with one another. At least one of the fill yarns is provided as a shrinkable yarn that provides the wall with an ability to remain in a first, diametrically enlarged assembly state to facilitate assembly of the sleeve about the elongate member, whereupon the wall can be radially constricted to a second, diametrically constricted assembled state to maintain the sleeve in the desired location, while also minimizing the outer circumference to facilitate use of the sleeve in tight spaces.