A compression assembly is adapted for placement on a body part for imparting compression therapy to the body part. The compression assembly includes a bladder and a bladder support. The bladder support and bladder have corresponding connection structure for mounting the bladder on the bladder support. In certain embodiments, the bladder is held in tension when mounted on the bladder support. In certain embodiments, the bladder support includes protrusions adapted for push-in reception in openings on the bladder for mounting the bladder on the bladder support, the bladder support is adjustable in length, and the bladder is foldable for adjusting the length of the bladder. Removable mounting of the bladder on the bladder support enables selective disposal of the bladders and bladder supports and interchangeability of different types of bladders with particular bladder supports.
