Provided herein are polymeric α-hydroxy aldehyde or α-hydroxy ketone reagents which can be conjugated to amine-containing compounds to form stable conjugates in a single-step reaction. In selected embodiments, the polymeric reagent itself incorporates an internal proton-abstracting (basic) functional group, to promote more efficient reaction. The substituent is appropriately situated, via a linker if necessary, to position the group for proton abstraction, preferably providing a 4- or 5-bond spacing between the abstracting atom and the hydrogen atom on the α-carbon. Also provided are methods of using the reagents and stable, solubilized conjugates of the reagents with biologically active compounds. In preferred embodiments, the polymeric component of the reagent or conjugate is a polyethylene glycol.