The invention relates to a tire having a circumferential rubber tread of a cap/base construction composed of a cap rubber layer as the tire running surface and an internal base rubber layer underlying said tread cap layer. The said tread cap layer is composed of a primary tread cap portion and one or two lateral tread cap portions of rubber compositions containing precipitated silica and/or rubber reinforcing carbon black reinforcement and wherein the rubber composition of at least one of said lateral tread cap portions contains a dispersion of short carbon fibers. Said primary tread cap portion contains a major portion of the running surface of the tread and is comprised of a silica-rich or carbon black-rich, preferably silica-rich, reinforcement-containing rubber composition, and said lateral tread portion(s) contains a minor portion of the running surface of the tread and is comprised of a silica-rich or carbon black-rich, preferably carbon black-rich, reinforcement-containing rubber composition. Where said primary tread cap portion is comprised of a silica-rich rubber composition, said lateral tread cap portion(s) is comprised of a carbon black-rich rubber composition and visa versa. The said tread cap portions are load bearing portions in the sense of extending from the running surface of the tread radially inward to said underlying tread base layer. In one aspect, the portioned rubber tread cap layer and the rubber tread base layer are co-extruded together to form a unitary composite thereof.