A method for modifying asphalt comprises blowing an oxygen-containing gas through a base asphalt at a high gas flow rate while simultaneously agitating the base asphalt at a high shear rate and at an elevated temperature for a period of time that is effective to substantially improve at least two paving properties of the base asphalt. In preferred embodiments, modified asphalts are produced having both substantially improved rutting resistance and substantially improved fatigue resistance as compared to the base asphalt.