This paper describes the methodology and practice-based research underpinning the development of a successful cleaning strategy for Eva Hesse's sculpture Addendum (1967, Tate Collection T02394). Research strands included: technical and art historical investigations to determine the materials and construction of the work of art and to define the aims of the conservation treatment; the production, soiling and accelerated ageing of mock-up samples using contemporary equivalent materials; and the systematic, iterative evaluation of soiling removal systems, which were further refined for appropriate use on the work of art. The comparative cleaning system evaluation was employed to determine options which offered optimal soiling removal efficacy and posed minimal risk to the work of art. Newly developed Nanorestore Gel ® Peggy series (i.e. polyvinyl alcohol (PVA) and polyvinyl alcohol/polyvinylpyrrolidone (PVA/PVP)-based hydrogels), designed for the cleaning of modern and contemporary art, were evaluated with a range of other gels, emulsifiers and cosmetic sponges and assessed through a combination of empirical observation, microscopy and spectroscopic techniques. Promising options, combined with tailored aqueous phases derived from trials on mock-up samples, were then evaluated on discreet areas of the sculpture. After extensive testing, the top papier mâché section of Addendum was surface cleaned using an aqueous solution applied with cosmetic sponges, and the ropes were surface cleaned using a modified version of Nanorestore Gel ® Peggy 5 (PVA/PVP) loaded with a tailored aqueous solution. The optimisation of this hydrogel, combined with the extensive supporting research, enabled the successful, low-risk, conservation treatment of Addendum for the first time since acquisition.