This invention discloses a rubbery polymer which is comprised of repeat units that are derived from (1) at least one conjugated diolefin monomer, and (2) 0.1 weight percent to 2 weight percent of at least one monomer having the structural formula: ##STR00001## wherein R represents an alkyl group containing from 1 to about 10 carbon atoms or a hydrogen atom, wherein R' represents a methyl group or a hydrogen atom, with the proviso that if R represents an alkyl group then R' represents a hydrogen atom, wherein R.sup.1 and R.sup.2 can be the same or different, wherein R.sup.1 represents an alkyl group that is functionalized with a leaving group, wherein R.sup.2 represents a moiety selected from the group consisting of hydrogen atoms, alkyl groups containing from 1 to 18 carbon atoms, aryl groups containing from 6 to 18 carbon atoms, alkaryl groups containing from 7 to 18 carbon atoms, and alkyl groups that are functionalized with a leaving group, wherein the rubbery polymer is void of moieties containing tertiary amine groups, and wherein the rubbery polymer is void of repeat units which are derived from .alpha.,.beta.-olefinically unsaturated amides.