A pneumatic tire including a circumferential tread, two spaced apart beads, and sidewalls connecting said beads and tread, wherein said tire sidewall contains at least one internal annular sidewall insert including at least two annular segments, the at least two annular segments including first and second adjacent annular segments; wherein said first and second annular segments are disposed with an interface therebetween; wherein each of the at least two annular segments includes a rubber composition comprising at least one diene based rubber and at least one vulcanization modifier selected from the group consisting of .alpha.,.omega.-bis(N,N'-dihydrocarbylthiocarbamamoyldithio)alkanes, bismaleimides, and biscitraconimides; and wherein the concentration of vulcanization modifier in the first annular segment is less than the concentration of vulcanization modifier in the second annular segment.