An insulin analogue comprises a B-chain polypeptide containing at least one alteration selected from a methylated phenylalanine substitution at position B24 and an addition of two amino acids to the carboxyl end of the B-chain polypeptide. A first amino acid at position B31 is selected from glutamate and aspartate, and a second amino acid at position B32 is selected from glutamate, alanine and aspartate. The methylated phenylalanine may be ortho-monofluoro-phenylalanine, meta-monobromo-phenylalanine or para-monochloro-phenylalanine. The analogue may be an analogue of a mammalian insulin, such as human insulin. A nucleic acid encoding such an insulin analogue is also provided. A method of treating a patient comprises administering a physiologically effective amount of the insulin analogue or a physiologically acceptable salt thereof to a patient.