The present invention provides a compound or a pharmaceutically acceptable salt of the Formula : X1 I V X2 S L D V P I G L L Q I L X3 E Q E K Q E K E K Q Q A K* T N A X4 I L A Q V-NH2 wherein the X1 denotes that the I residue is modified by either acetylation or methylation at the N-terminus； wherein X2 is L or T； wherein X3 is L or I； wherein X4 is 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 -X-5X6, wherein X5 is 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-Aminoethoxy)- ethoxy]-acetyl) moieties； and X6 is a C14-C24 fatty acid. In some embodiments, the group of the formula -X5 -X6 is ([2- (2-Amino-ethoxy)-ethoxy]-acetyl)2-(#E)2-CO-(CH2)x-CO2H where x is 16 or 18.
