A thermoplastic vulcanizate comprising a dynamically-cured rubber, where the rubber is selected from the group consisting of ethylene-propylene-non-conjugated diene rubber, propylene-based rubbery copolymers with units derived from non-conjugated diene monomers, butyl rubber and styrene-butadiene rubber, where dynamic vulcanization is effected with a phenolic resin or a silicon-containing curative, and where the rubber is dynamically cured to an extent where greater than 94% by weight of the rubber is insoluble in cyclohexane at 23° C., and from about 25 to about 250 parts by weight of a thermoplastic polymer phase per 100 parts by weight rubber, where about 85% to about 50% by weight of the thermoplastic polymer phase includes a propylene-based polymer, and where from about 15% to about 50% by weight of the thermoplastic polymer phase includes a butene-1-based polymer.