This application relates to a prosthesis 12 and a cover 1 for a residual limb, wherein: the cover 1 comprises a first region 8 that is normally of a greater circumference than an adjacent second region of the cover, said first region being resiliently deformable so as to temporarily reduce the circumference of that region of the cover, and the prosthesis 12 comprises a portion that defines an internal cavity 11 into which a residual limb that is at least partly covered by said cover 1 may be inserted, wherein said cavity 1 1 is configured to include a first region 13 that has a first cross-sectional area and below said first region in the direction of limb insertion, a second region 15 that has a second cross-sectional area larger than said first, the arrangement being such that said resiliently deformable first region 8 of said cover deforms to reduce the circumference of that region of said cover as the cover 1 moves through said first region 13 of the cavity, and expands in said second region 15 of the cavity to thereby couple the prosthesis 12 to the user's covered residual limb. A cover with a nipple and a prosthesis with a complementary socket are also disclosed.