Sidewalls of a pneumatic tire have greater resistance to failure due to dynamic flexing and abrasion, and the tire's tread has better resistance to tearing than with conventionally used rubber compositions, when sidewalls and tread are formed from a compound having a major proportion by weight of synthetic rubber (SR) and a minor proportion by weight of natural rubber (NR), and a major proportion by weight of the SR itself consists essentially of a high cis-1,4-polybutadiene having defined molecular architecture. The high cis-1,4-PBD has more than 90 percent cis-structure, a poly-dispersity in the range from about 3 to 5, a number average molecular weight Mn in the range from 100,000 to 150,000 and a degree of branching in the range from 2 to 3.5. The sidewall compound has characteristics quite different from one made with a typical commercially available high cis-1,4-PBD; and the tread has excellent tear strength. The dendritic structure of the high HI cis-1,4-PBD molecules has an unexpectedly beneficial effect on the performance characteristics of the sidewall and tread, particularly important in a high-performance automobile tire.