The packaging industry desires adhesive compositions having a fast set time, such as those setting in less than five seconds from a molten state at conventional packaging operating temperatures to a solid or quasi solid having favorable Dot T-Peel, set time, and/or fiber tear adhesion properties. Polymer based adhesives performing within this window are a favorable alternative to conventional formulated adhesives. The provided adhesive compositions exhibit a favorable balance of properties such as high adhesive strength, wide temperature operating window, and fast set time. Provided are adhesive compositions composed of a polyolefin composition comprising at least about 50 mol % polypropylene, at least one wax and at least one wax modifier.