A compound having the formula I: R 1 -Z-R 2 or a pharmaceutically acceptable salt or solvate thereof; wherein R 1 is hydrogen, C 1-4 alkyl, acetyl, formyl, benzoyl or trifluoroacetyl; R 2 is OH or NH 2; and Z is an amino acid sequence deriving from the sequence of formula Ia: and further comprising at least four amino acid substitutions or deletions that are only at sequence positions selected from 2, 3, 4, 9, 10, 15, 16, 17, 20, 21, 24, 28 and 29, as follows: X2 is selected from Aib and Ala; X3 is selected from His, Pro, Dab(Ac), Dap(Ac) and Gln(Me); X4 is DAla; X9 is Glu; X10 is selected from Val, Leu, N-Me-Tyr and N-Me-DTyr; X15 is Glu; X16 is selected from Aib, Lys, Glu, Leu, Val, DVal, Phe, His, Arg, Pro, DPro, N-Me-Ser and N-Me-DSer; X17 is selected from Ala and Ser; X20 is selected from Glu and Lys; X21 is selected from Glu, Lys and Ser; X24 is selected from Lys, Ser, Glu and Ala; X28 is selected from Ser and Lys, and Glu, or is absent; X29 is selected from Ser and Ala, or is absent;with the proviso that Z is not selected from: HSQGTFTSDYSKYLDSARAEDFVKWLEST; and HSQGTFTSDYSKYLESRRAKEFVEWLEST; wherein the compound has glucagon agonist activity and improved solubility and/or stability as compared to native human glucagon. R 1 is hydrogen, C 1-4 alkyl, acetyl, formyl, benzoyl or trifluoroacetyl; R 2 is OH or NH 2; and Z is an amino acid sequence deriving from the sequence of formula Ia: and further comprising at least four amino acid substitutions or deletions that are only at sequence positions selected from 2, 3, 4, 9, 10, 15, 16, 17, 20, 21, 24, 28 and 29, as follows: X2 is selected from Aib and Ala; X3 is selected from His, Pro, Dab(Ac), Dap(Ac) and Gln(Me); X4 is DAla; X9 is Glu; X10 is selected from Val, Leu, N-Me-Tyr and N-Me-DTyr; X15 is Glu; X16 is selected from Aib, Lys, Glu, Leu, Val, DVal, Phe, His, Arg, Pro, DPro, N-Me-Ser and N-Me-DSer; X17 is selected from Ala and Ser; X20 is selected from Glu and Lys; X21 is selected from Glu, Lys and Ser; X24 is selected from Lys, Ser, Glu and Ala; X28 is selected from Ser and Lys, and Glu, or is absent; X29 is selected from Ser and Ala, or is absent;with the proviso that Z is not selected from: HSQGTFTSDYSKYLDSARAEDFVKWLEST; and HSQGTFTSDYSKYLESRRAKEFVEWLEST; wherein the compound has glucagon agonist activity and improved solubility and/or stability as compared to native human glucagon. X2 is selected from Aib and Ala; X3 is selected from His, Pro, Dab(Ac), Dap(Ac) and Gln(Me); X4 is DAla; X9 is Glu; X10 is selected from Val, Leu, N-Me-Tyr and N-Me-DTyr; X15 is Glu; X16 is selected from Aib, Lys, Glu, Leu, Val, DVal, Phe, His, Arg, Pro, DPro, N-Me-Ser and N-Me-DSer; X17 is selected from Ala and Ser; X20 is selected from Glu and Lys; X21 is selected from Glu, Lys and Ser; X24 is selected from Lys, Ser, Glu and Ala; X28 is selected from Ser and Lys, and Glu, or is absent; X29 is selected from Ser and Ala, or is absent;with the proviso that Z is not selected from: HSQGTFTSDYSKYLDSARAEDFVKWLEST; and HSQGTFTSDYSKYLESRRAKEFVEWLEST; wherein the compound has glucagon agonist activity and improved solubility and/or stability as compared to native human glucagon. HSQGTFTSDYSKYLDSARAEDFVKWLEST; and HSQGTFTSDYSKYLESRRAKEFVEWLEST;