An insulin analogue comprises an insulin B-chain polypeptide modified with an O-linked monosaccaride pyranoside adduct at the side chain of residue B27 or an O-linked monosaccaride pyranoside adduct at the side chain of residue B30, or both, where the positions are recited relative to human insulin. The monosaccaride may be a manopyranoside, an N-acetyl-galactopyranoside, or a glucopyranoside. The insulin analogue may additionally comprise containing a foreshortened B-chain polypeptide lacking residues B1-B3, an extension of 1 or 2 Glu residues on the carboxy terminal end of the B-chain polypeptide, an extension of ornithine at the carboxy-terminal end of the B-chain, the substitutions Lys at position B28 and Pro at position B29, an ornithine substitution at position B29, or combinations thereof. The analogue may be an analogue of a mammalian insulin, such as human insulin. A method of treating a patient comprises administering a physiologically effective amount of the insulin analogue.