The present invention provides a compound or a pharmaceutically acceptable salt of the Formula:X1IVX2SLDVPIGLLQILX3EQEKQEKEKQQAK*TNAX4ILAQV-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 —X5—X6, 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-Amino-ethoxy)-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-(γE)2-CO—(CH2)x—CO2H where x is 16 or 18.
