We present our results obtained in the Rh-catalyzed carbene copolymerization of diazomethane and diazoesters as a new approach to functional polymer synthesis. Copolymerization reactions were successful, and high-M-w ethylene-acrylate type copolymers were obtained with a large variation in functional group content, which proved to be tunable by varying the monomer feed ratio and the way of addition. Polymer yields decrease strongly with increasing incorporation of diazomethane due to rapid beta-hydride elimination. Sequential insertions of polar monomers were observed to a large extent, giving rise to copolymers with a blocky microstructure, which is a unique feature of this polymerization technique. The copolymer properties are demonstrated to be highly dependent on the functional group content and can therefore easily be varied in the window between the properties of both homopolymers.