The subject invention provides a method for producing essentially homogeneous asphalt compositions which are comprised of the asphalt, a block copolymer (such as a linear block copolymer or a radial block copolymer), and one or more additional desired additives. This method offers the advantage of being capable of attaining the essentially homogeneous asphalt composition in one pass procedure with a short residence time in the mixing equipment. This greatly reduces the thermal history to which heat sensitive asphalt additives, such as asphalt modification polymers, are exposed. It also simplifies the mixing procedure and can reduce the overall amount of energy required to attain the desired blend. In some case, it allows for the production on a commercial basis of asphalt compositions which would otherwise not be feasible, for instance the production of asphalt compositions which contain high levels of asphalt modifications polymers which are otherwise difficult to process.