An insulin analog comprising an A chain, a B chain and a dipeptide element, wherein said A chain has the general formula Z-peptide A, wherein peptide A comprises the sequence of GIVEQCCX 1 SICSLYQLENX 2 CX 3 (SEQ ID NO: 3), or an analog thereof comprising a sequence that differs from SEQ ID NO: 3 by 1 to 3 amino acid modifications, selected from positions A5, A8, A9, A10, A14, A15, A17, and A18; and said B chain has the general formula J-X 14 -peptide B, wherein peptide B comprises a sequence of X 4 LCGX 5 X 6 LVEALX 7 LVCGERGFX 8 (SEQ ID NO: 14), or an analog thereof comprising a sequence that differs from SEQ ID NO: 14 sequence by 1 to 3 amino acid modifications, selected from positions B5, B13, B14, B17, B20, B22, and B23 said B chain being linked to said A chain through intermolecular disulfide linkages, wherein Z and J are independently H or a dipeptide element of the structure of Formula I; X 1 is selected from the group consisting of threonine and histidine; X 2 is an amino acid of the structure of: wherein m is an integer selected from the group consisting of 0-3; X is selected from the group consisting of OH, OCH 3, NH 2 and NHR 10, wherein R 10 is a dipeptide element comprising the general structure of Formula I; X 3 is selected from the group consisting of asparagine, glycine and alanine, threonine and serine; X 4 is selected from the group consisting of histidine and threonine; X 5 is selected from the group consisting of alanine, glycine and serine; X 6 is selected from the group consisting of histidine, aspartic acid, glutamic acid, homocysteic acid and cysteic acid; X 7 is an amino acid of the general structure wherein m is an integer selected from 0-3 and X 12 is selected from the group consisting of OH, NH 2, NHR 11 and OCH 3, wherein R 1 is a dipeptide element comprising the structure of Formula I; X 8 is an amino acid of the general structure wherein m is an integer selected from 0-3 and X 13 is selected from the group consisting of H, OH, NH 2, NHR 12 and OCH 3, wherein R 12 is a dipeptide element of the structure of Formula I; X 14 is selected from the group consisting of a bond, X 9 VNQ (SEQ ID NO: 21), VNQ, NQ and Q, wherein X 9 is selected from the group consisting of phenylalanine and desamino-phenylalanine; said dipeptide element being linked to said A or B chain through formation of an amide bond wherein the chemical cleavage half-life (t 1/2) of said dipeptide from said A or B chain is at least about 1 hour to about 1 week in PBS under physiological conditions said dipeptide element having the general structure of Formula I: wherein R 1, R 2, R 4 and R 8 are independently selected from the group consisting of H, C 1 -C 18 alkyl, C 2 -C 18 alkenyl, (C 1 -C 18 alkyl)OH, (C 1 -C 18 alkyl)SH, (C 2 -C 3 alkyl)SCH 3, (C 1 -C 4 alkyl)CONH 2, (C 1 -C 4 alkyl)COOH, (C 1 -C 4 alkyl)NH 2, (C 1 -C 4 alkyl)NHC(NH 2 +)NH 2, (C 0 -C 4 alkyl)(C 3 -C 6 cycloalkyl), (C 0 -C 4 alkyl)(C 2 -C 5 heterocyclic), (C 0 -C 4 alkyl)(C 6 -C 10 aryl)R 7, (C 1 -C 4 alkyl)(C 3 -C 9 heteroaryl), and C 1 -C 12 alkyl(W 1)C 1 -C 12 alkyl, wherein W 1 is a heteroatom selected from the group consisting of N, S and 0, or R 1 and R 2 together with the atoms to which they are attached form a C 3 -C 12 cycloalkyl; or R 4 and R 8 together with the atoms to which they are attached form a C 3 -C 6 cycloalkyl; R 3 is selected from the group consisting of C 1 -C 18 alkyl, (C 1 -C 18 alkyl)OH, (C 1 -C 18 alkyl)NH 2, (C 1 -C 18 alkyl)SH, (C 0 -C 4 alkyl)(C 3 -C 6)cycloalkyl, (C 0 -C 4 alkyl)(C 2 -C 5 heterocyclic), (C 0 -C 4 alkyl)(C 6 -C 10 aryl)R 7, and (C 1 -C 4 alkyl)(C 3 -C 9 heteroaryl) or R 4 and R 3 together with the atoms to which they are attached form a 4, 5 or 6 member heterocyclic ring; R 5 is NHR 6 or OH; R 6 is H, C 1 -C 8 alkyl or R 6 and R 1 together with the atoms to which they are attached form a 4, 5 or 6 member heterocyclic ring; and R 7 is selected from the group consisting of hydrogen and OH; and R 13 is COOH or CONH 2, with the proviso that one or more of X, X 12, X 13, J and Z is a dipeptide element of the structure of Formula I and at least one of R 1 and R 2 is other than H.