An asphalt material having improved paving characteristics and processes for its preparation. An asphalt base material is heated in a mixing chamber to a temperature sufficient to melt the asphalt so that it can be stirred. A water-insoluble heavy metal soap is incorporated into the chamber in an amount effective to reduce the PAV-DSR temperature of the asphalt base material by an incremental amount of at least 1° C. Thereafter, the asphalt material is recovered from the mixing chamber to provide an asphalt product containing the heavy metal soap which exhibits a PAV-DSR temperature which is less than the PAV-DSR temperature for the corresponding base material without the addition of the heavy metal soap. The water-insoluble soap is a C14-C18 heavy metal soap such as a C16-C18 zinc- or calcium-based soap including zinc stearate, zinc oleate and zinc palmitate. The heavy metal soap is added to the mixing chamber in an amount within the range of 0.05-3.0 wt. % of the amount of asphalt based material in the mixing chamber. A thermoplastic polymer may be added to the asphalt based material to provide a polymer-modified asphalt blend. An asphalt paving composition comprising an asphalt base material and a water-insoluble heavy metal soap in an amount to provide a PAV-DSR temperature lower than the PAV-DSR temperature of the corresponding asphalt material without the addition of the heavy metal soaps.