in a process for manufacturing degradable cigarette filters wherein adhesive is applied to at least one longitudinal edge of the plug wrap paper , a bond is made while the adhesive is molten and the resultant bond is held in compression for sufficient time to prevent bond movement , the improvement which comprises , using as the adhesive , a water sensitive hot melt adhesive comprising 50 to 90 weight percent of a graft copolymer which copolymer comprises 40 to 85 weight percent of at least one vinyl monomer and 15 to 60 weight percent of at least one polyalkylene oxide polymer , 0 to 50 weight percent of a compatible tackifying resin , 5 to 40 weight percent of a polar wax , 0 to 3 weight percent antioxidant and 0 to 30 weight percent of another compatible water soluble or water sensitive thermoplastic polymer ; characterized in that the resulting cigarette filter will open when exposed to moisture .