A method of treating a patient includes administering a physiologically effective amount of an insulin analogue or a physiologically acceptable salt thereof to the patient. The insulin analogue or physiologically acceptable salt thereof contains an insulin A-chain sequence modified at positions selected from the group consisting of A0, A1, A4, A8, and A21. The insulin analogue may exhibit decreased affinity for the IGF receptor in comparison to wild type insulin of the same species and at least 20% of the affinity of wild-type insulin for the insulin receptor of the same species. Position A0 may be arginine. Position A1 may be D-alanine, D-aspartic acid, or D-leucine. Position A8 may be histidine, lysine, or arginine. Optionally, an insulin B-chain analogue sequence comprises a histidine at position B1. A nucleic acid may encode such an insulin polypeptide.
