We report the development of a new type of hydrogel in which a cosolvent has been added to the water component. The gel networks are based on the well-known poly(vinyl alcohol)-borate systems (PVA-borate). However, it is shown that the rheological and solubilizing properties of the hydrogels can be modified drastically by the addition of a cosolvent. The studies have focused on 1-propanol as the added liquid, although it is shown that others (propylene carbonate, 1-pentanol, cyclohexanone, and 2-butanol) are amenable to making modified hydrogels as well. In addition to the rheological measurements, the gels have been investigated by differential scanning calorimetry (free water index) and determination of their solubilizing power. Finally, the gels have been applied to clean and oxidized varnish (patina) from the surface of a XVI-XVII century oil-on-wood painting by Ludovico Cardi detto il Cigoli. The mode of cleaning by and removal of the PVA-borate water/1-propanol gel from the painted surface demonstrate several advantages over other gels used in art conservation.