Provided are adhesive compositions composed of a polyolefin composition comprising at least about 50 wt. % polypropylene and at least one wax. The polymer compositions have a Dot T-Peel of about 1 Newton or more, a branching index (g′) of 0.95 or less measured at the Mz of the polymer, a molecular weight of 100,000 or less, and the adhesive compositions has a fast set time. 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.