Disclosed herein are devices and methods for reduced pressure tissue therapy. Some variations of suction devices for reduced pressure tissue therapy comprise a housing, a suction force generating mechanism located within the housing, and a storage module configured to retain tissue exudates. In some variations, the storage module includes a sleeve configured to collect tissue exudates. The sleeve may include a support element to help maintain the lateral structural integrity of the sleeve and/or retain the cross-sectional geometry of the sleeve under negative pressure. In use, the storage module may reduce sanitary and/or biohazard risks by preventing the exudates from contacting the housing and/or suction force generating mechanism. The storage module is configured to be replaced so that the housing and suction force generating mechanism can be used for more than one session.