A compression device (10, 600, 700, 740, 760, 780, 790, 795, 800, 810, 920, 935, 937, 1010, 1050) for applying controllable compression to a portion of the anatomy of a user, comprising: a panel formed of a wearable material, the panel (12, 602, 610, 704, 811-816) sized and configured to be applied to a portion of the anatomy of the user, the panel having opposite ends configured to oppose each other when the panel is applied to the portion of the anatomy; a plurality of shape memory wires ( 14, 705, 910, 915, 936, 938, 1001, 1020, 1054) supported by the panel between said opposite ends and configured to apply a compressive force to the portion of the anatomy of the user; a pre-tensioning apparatus (62, 620, 706, 711, 820) connectable between said opposite ends when the panel is applied to the portion of the anatomy, the pre-tensioning apparatus operable to draw the opposite ends toward each other to thereby apply an initial tension to the panel and/or the plurality of shape-memory wires; and a controller (24, 66, 1065) configured to selectively actuate one or more of the plurality of shape-memory wires to reduce the effective length of the wires and thus the panel about the portion of the anatomy, to thereby apply pressure to the portion of the anatomy of the user, characterized in that each of said plurality of shape-memory wires is disposed within an elastomeric sheath (714, 1003, 1022), wherein the sheath (714, 1003, 1022) is formed of silicone or a polyurethane material, wherein the sheath material is doped with a thermally conductive or thermally insulative material to adjust the overall conductivity of the sheath(714, 1003, 1022), to have a thermal conductivity sufficient to help the shape memory wire (14, 705, 910, 915, 936, 938, 1001, 1020, 1054) maintain its temperature upon contraction with only limited additional energy input required to maintain the same level of compression. a panel formed of a wearable material, the panel (12, 602, 610, 704, 811-816) sized and configured to be applied to a portion of the anatomy of the user, the panel having opposite ends configured to oppose each other when the panel is applied to the portion of the anatomy; a plurality of shape memory wires ( 14, 705, 910, 915, 936, 938, 1001, 1020, 1054) supported by the panel between said opposite ends and configured to apply a compressive force to the portion of the anatomy of the user; a pre-tensioning apparatus (62, 620, 706, 711, 820) connectable between said opposite ends when the panel is applied to the portion of the anatomy, the pre-tensioning apparatus operable to draw the opposite ends toward each other to thereby apply an initial tension to the panel and/or the plurality of shape-memory wires; and a controller (24, 66, 1065) configured to selectively actuate one or more of the plurality of shape-memory wires to reduce the effective length of the wires and thus the panel about the portion of the anatomy, to thereby apply pressure to the portion of the anatomy of the user, characterized in that each of said plurality of shape-memory wires is disposed within an elastomeric sheath (714, 1003, 1022), wherein the sheath (714, 1003, 1022) is formed of silicone or a polyurethane material, wherein the sheath material is doped with a thermally conductive or thermally insulative material to adjust the overall conductivity of the sheath(714, 1003, 1022), to have a thermal conductivity sufficient to help the shape memory wire (14, 705, 910, 915, 936, 938, 1001, 1020, 1054) maintain its temperature upon contraction with only limited additional energy input required to maintain the same level of compression.