The invention relates to a drainage device (100) for the treatment of wounds using reduced pressure, comprising (a) a gas-type wound-covering element (3), which, in the state in contact with the body of the patient, is fastened cohesively at the skin surface around the region of the wound and forms a sealed wound space, remaining between the respective wound and the wound-covering element (3); (b) at least one drainage tube (4), which can be connected to means generating the reduced pressure and can be inserted into the wound space approximately parallel to the wound-covering element (3); and (c) at least one absorption body (2) in the form of at least one layer (7) of a textile section (33), which is interspersed with super-absorbing particles and enclosed in an envelope. Due to the size of the pores of the envelope, the absorbed wound secretions remain within the absorption body (2) and, with that, underneath the wound-covering element (3) until the absorption body is removed from the wound space. An air opening (34) is provided for the wound-covering element (3).