A substantially gel free C.sub.4 to C.sub.7 isoolefin homopolymer rubber, butyl copolymer rubber, halogenated butyl rubber (e.g., chlorinated or brominated), or mixtures thereof, comprising a molecular weight distribution such that the ratio of the moments of said molecular weight distribution, Mz/Mw, is equal to or exceeds 2.0, and that portion of said molecular weight distribution which is equal to and greater than 4 times the peak molecular weight, Mp, comprises greater than 8 percent of the total polymer species, and Mp is greater than about 250,000 and wherein said polymer species of molecular weight less than Mp are substantially branch free. Various means are disclosed for effecting the molecular weight distribution including blending of homopolymers and/or copolymers of appropriate molecular weight and molecular weight distribution and direct polymerization using a functional reagent to introduce branching. The rubber compositions are particularly useful in applications in which butyl or halogenated butyl rubber is used and where it is desired to obtain high green strength in combination with an increased rate of stress relaxation. Such polymers are particularly well suited for use in tire innerliner compositions.