The invention provides a polymer comprising (i) a first water-soluble polymer segment that is covalently attached, either directly or through one or more atoms, to a first oxygen atom that is covalently attached to a linking carbon atom; (ii) a second water-soluble polymer segment is covalently attached, either directly or through one or more atoms, to a second oxygen atom that is covalently attached to the linking carbon atom; and (iii) a reactive group that is covalently attached, either directly or through one or more atoms, to the linking carbon atom. The invention also provides, among other things, methods for preparing polymers, conjugates, pharmaceutical compositions and the like.