A compression garment for applying compression to a part of a wearer's body, the garment comprising: a layer of material (12, 14, 16, 18) sized and shaped for wrapping around the body part such that the layer of material (12, 14, 16, 18) encircles and conforms to the body part, the layer of material (12, 14, 16, 18) comprising an inner layer, a first intermediate layer, a second intermediate layer and an outer cover; a bladder formed of the first intermediate layer and the second intermediate layer, the bladder being secured to the inner layer and to the outer cover, wherein the bladder comprises openings; wherein the compression garment further comprises: a stay up device (90, 90') operatively connected to the layer of material (12, 14, 16, 18) for supporting the layer of material (12, 14, 16, 18) against movement along a length of the body part, wherein the stay up device is disposed between the first intermediate layer and the inner layer, the stay up device (90, 90') including: a first region (100, 100') having holes, a second region (102, 102') and at least one leg portion (106, 106') extending between and interconnecting the first and second regions (100, 102, 100', 102'), the second region (102, 102') being adapted to operatively engage a portion of the wearer's body adjacent to the second region for locating the stay up device (90, 90') relative to the wearer's body to support the layer of material (12, 14, 16, 18) in a generally fixed location relative to the body, wherein the holes in the first region (100, 100') are generally aligned with the openings in the bladder. a layer of material (12, 14, 16, 18) sized and shaped for wrapping around the body part such that the layer of material (12, 14, 16, 18) encircles and conforms to the body part, the layer of material (12, 14, 16, 18) comprising an inner layer, a first intermediate layer, a second intermediate layer and an outer cover; a bladder formed of the first intermediate layer and the second intermediate layer, the bladder being secured to the inner layer and to the outer cover, wherein the bladder comprises openings; wherein the compression garment further comprises: a stay up device (90, 90') operatively connected to the layer of material (12, 14, 16, 18) for supporting the layer of material (12, 14, 16, 18) against movement along a length of the body part, wherein the stay up device is disposed between the first intermediate layer and the inner layer, the stay up device (90, 90') including: a first region (100, 100') having holes, a second region (102, 102') and at least one leg portion (106, 106') extending between and interconnecting the first and second regions (100, 102, 100', 102'), the second region (102, 102') being adapted to operatively engage a portion of the wearer's body adjacent to the second region for locating the stay up device (90, 90') relative to the wearer's body to support the layer of material (12, 14, 16, 18) in a generally fixed location relative to the body, a first region (100, 100') having holes, a second region (102, 102') and at least one leg portion (106, 106') extending between and interconnecting the first and second regions (100, 102, 100', 102'), the second region (102, 102') being adapted to operatively engage a portion of the wearer's body adjacent to the second region for locating the stay up device (90, 90') relative to the wearer's body to support the layer of material (12, 14, 16, 18) in a generally fixed location relative to the body, wherein the holes in the first region (100, 100') are generally aligned with the openings in the bladder.