A rubber composition comprising: a bifunctionalized elastomer comprising the reaction product of 1) a living anionic elastomeric polymer initiated with a functional initiator and 2) a functional polymerization terminator, wherein the living anionic elastomeric polymer initiated with a functional initiator is of formula AYLi where Y is a divalent polymer radical, Li is a lithium atom bonded to a carbon atom of Y, and A is an amine-containing radical having the formula X wherein R 15 and R 16 independently have from 1 to 20 carbon atoms and each are independently an alkyl group, a cycloalkyl group, an aromatic group, a substituted alkyl group, a substituted cycloalkyl group or a substituted aromatic group, or R 15 and R 16 taken together with the nitrogen to which both R 15 and R 16 are attached comprise a heterocyclic amine group wherein R 15 and R 16 taken together form an alkanediyl group of from 4 to 20 carbon atoms or a substituted alkanediyl group of from 4 to 20 carbon atoms, and R 17 is a covalent bond, an alkanediyl group of from 1 to 20 carbon atoms or a substituted alkanediyl group of from 1 to 20 carbon atoms; and the functional polymerization terminator is of formula I wherein R 1 is C1 to C4 linear alkyl, or C1 to C4 branched alkanediyl; X 1, X 2, X 3 are independently O, S, or a group of formula or where R 2 is C1 to C18 linear or branched alkyl; Z is R 3, -OR 4, or -R 5 -X 4; R 3, R 4 are independently C1 to C18 linear or branched alkyl; R 5 is C1 to C18 alkanediyl or dialkyl ether diyl; X 4 is halogen or a group of structure IV, V, VI, VII or VIII wherein R 6, R 7, R 8, R 9, and R 10 are independently H or C1 to C8 alkyl; R 11 is C2 to C8 alkanediyl; R 12 and R 13 are independently H, aryl or C1 to C8 alkyl; Q is N or a group of structure IX wherein R 14 is C1 to C8 alkyl. a bifunctionalized elastomer comprising the reaction product of 1) a living anionic elastomeric polymer initiated with a functional initiator and 2) a functional polymerization terminator, wherein the living anionic elastomeric polymer initiated with a functional initiator is of formula AYLi where Y is a divalent polymer radical, Li is a lithium atom bonded to a carbon atom of Y, and A is an amine-containing radical having the formula X wherein R 15 and R 16 independently have from 1 to 20 carbon atoms and each are independently an alkyl group, a cycloalkyl group, an aromatic group, a substituted alkyl group, a substituted cycloalkyl group or a substituted aromatic group, or R 15 and R 16 taken together with the nitrogen to which both R 15 and R 16 are attached comprise a heterocyclic amine group wherein R 15 and R 16 taken together form an alkanediyl group of from 4 to 20 carbon atoms or a substituted alkanediyl group of from 4 to 20 carbon atoms, and R 17 is a covalent bond, an alkanediyl group of from 1 to 20 carbon atoms or a substituted alkanediyl group of from 1 to 20 carbon atoms; and the functional polymerization terminator is of formula I wherein R 1 is C1 to C4 linear alkyl, or C1 to C4 branched alkanediyl; X 1, X 2, X 3 are independently O, S, or a group of formula or where R 2 is C1 to C18 linear or branched alkyl; Z is R 3, -OR 4, or -R 5 -X 4; R 3, R 4 are independently C1 to C18 linear or branched alkyl; R 5 is C1 to C18 alkanediyl or dialkyl ether diyl; X 4 is halogen or a group of structure IV, V, VI, VII or VIII wherein R 6, R 7, R 8, R 9, and R 10 are independently H or C1 to C8 alkyl; R 11 is C2 to C8 alkanediyl; R 12 and R 13 are independently H, aryl or C1 to C8 alkyl; Q is N or a group of structure IX wherein R 14 is C1 to C8 alkyl.