The present invention provides a compound or a pharmaceutically acceptable salt of the Formula :wherein the X1denotes that the I residue is modified by either acetylation or methylation at the N-terminus； wherein X2is L or T； wherein X3is L or I； wherein X4is Q or E； and wherein a modified K residue (“K*”) at position 29 is modified through conjugation to the epsilon-amino group of the K-side chain with a group of the formula -X5-X6, wherein X5is selected from the group consisting of one to four amino acids； one to four ([2-(2-Amino-ethoxy)-ethoxy]-acetyl) moieties； and combinations of one to four amino acids and one to four ([2-(2-Amino-ethoxy)-ethoxy]-acetyl) moieties； and X6is a C14-C24fatty acid. In some embodiments, the group of the formula -X5-X6is ([2-(2-Amino-ethoxy)-ethoxy]-acetyl)2-(γE)2-CO-(CH2)x-CO2H where x is 16 or 18.本發明提供一種下式之化合物或醫藥學上可接受之鹽，其中X1表示I殘基在N端由乙醯化或甲基化修飾；其中X2係L或T；其中X3係L或I；其中X4係Q或E；且其中在位置29經修飾之K殘基(「K*」)係藉由式-X5-X6之基團結合於K側鏈之ε-胺基而修飾，其中X5係選自由以下組成之群：一至四個胺基酸；一至四個([2-(2-胺基-乙氧基)-乙氧基]-乙醯基)部分；及一至四個胺基酸與一至四個([2-(2-胺基-乙氧基)-乙氧基]-乙醯基)部分之組合；且X6係C14-C24脂肪酸。在一些實施例中，式-X5-X6之基團係([2-(2-胺基-乙氧基)-乙氧基]-乙醯基)2-(γE)2-CO-(CH2)x-CO2H，其中x為16或18。
