This invention relates to preparation of rubber compositions comprised of EPDM and conjugated diene-based elastomer, particularly including cis 1,4-polyisoprene rubber, and particularly natural cis 1,4-polyisoprene rubber, blends and pneumatic rubber tire with an outer, visible sidewall layer of a rubber composition comprised of such rubber composition. For such preparation, a combination of at least two diverse EPDM elastomers is used together with a phase mixing process comprised of sequential phase mixing or parallel phase mixing in the sense of reinforcement filler and sulfur curatives.