Conjugates of a GLP-I moiety may be covalently attached to one or more water-soluble polymers. For instance, a GLP-I polymer conjugate may include a GLP-I moiety releasably attached at its N-terminus to a water-soluble polymer. The GLP-I polymer conjugate may include a GLP-I moiety covalently attached to a water-soluble polymer, wherein the GLP-I moiety possesses an N-methyl substituent. The GLP-I polymer conjugate may include a GLP-I moiety covalently attached at a polymer attachment site to a water-soluble polymer, wherein the GLP-I moiety is glycosylated at a site separate from the polymer attachment site.
