Devices that employ external compression stocking-type garments in the treatment of edema, chronic wounds, deep venous thrombosis prevention or claudication all share a number of significant limitations. These include the frequent need for custom fitting to assure an appropriate fit, vigilant maintenance to assure a continued "good fit," limited compliance with proper use by patients and difficulty of application. There is a large body of evidence demonstrating that patients often decline to wear the compressive stockings as prescribed or in the form that would be most beneficial because they find these devices to be difficult to put on and take off. Building on the limitations of existing therapies, and distilled lessons learned from the field of prosthetics and wound healing, the present invention employs vacuum-assisted negative pressure to provide compression and help pump fluid from the tissues of affected limbs. The device is embodied in the form of a flexible stocking-like garment that will utilize a pumping mechanism to generate negative pressure around the limb and thus create vacuum compression that will mobilize fluid in a limb and increase venous return to the heart. Through the use of a circumferential wrap, the present invention provides a major advance in both the distribution of vacuum and the securing of the device over the limb.