An insulin analogue contains a foreshortened B-chain polypeptide lacking residues B1-B3 and optionally contains an additional substitution in the C-terminal B23-B30 segment of the B-chain. The insulin analogue lacking residues B1-B3 may contain substitutions at B28 and/or B29 that confer rapid action and optionally a non-standard substitution at B24. 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. A method of semi-synthesis is provided using an unprotected octapeptide by means of modification of an endogenous tryptic site by non-standard amino-acid substitutions.