Hot melt adhesive compositions which have enhanced adhesion to difficult substrates, particularly at refrigerator/freezer temperatures or at elevated temperatures. The inventive compositions require a base polymer comprising an ethylene vinyl acetate-containing polymer; a tackifier; an adhesion promoting additive comprising at least one semi-crystalline polymer having a weight average molecular weight of about 30,000 daltons or less; and optional wax; and an optional antioxidant. It has been found that the adhesion promoting additive of this invention enhances the adhesion properties of a hot melt adhesive composition having ethylene vinyl acetate-containing polymer, particularly at elevated temperatures or at low refrigerator and freezer temperatures where other conventional adhesives have been unsuccessful.