It has been determined that rubbery terpolymers of a conjugated diolefin monomer, a vinyl aromatic monomer, and N-(isobutoxymethyl) acrylamide (IBMA) tan be used to modify asphalt cement to greatly enhance the resistance to shoving, rutting, and low temperature cracking of asphalt concretes made therewith. These rubbery polymers have a Mooney viscosity which is within the range of about 35 to about 80. It has further been determined that these rubbery terpolymers are compatible with virtually all types of asphalt. It is particularly preferred for the rubbery polymers of this invention to also contain repeat units which are derived from hydroxypropyl methacrylate (HPMA). The subject invention more specifically relates to a modified asphalt cement which is comprised of (1) from about 90 weight percent to about 99 weight percent of asphalt; and (2) from about 1 weight percent to about 10 weight percent of a rubbery polymer which is comprised of repeat units which are derived from (a) about 64 weight percent to about 84.9 weight percent of a conjugated diolefin monomer, (b) about 15 weight percent to about 33 weight percent of a vinyl aromatic monomer, and (c) about 0.1 weight percent to about 3 weight percent of isobutoxymethyl acrylamide.