An amylin analogue which is a compound having the formula: R 1 -Z-R 2 wherein R 1 is hydrogen, C 1-4 acyl, benzoyl or C 1-4 alkyl, or a half-life extending moiety M, wherein M is optionally linked to Z via a linker moiety L; R 2 is OH or NHR 3, wherein R 3 is hydrogen or C 1-3 -alkyl; and Z is an amino acid sequence of formula I: X1-X2-X3-X4-X5-X6-X7-Ala-Thr-X10-Arg-Leu-Ala-X14-Phe-Leu-X17-Arg-X19-X20-Phe-Gly(Me)-Ala-Ile(Me)-X27-Ser-Ser-Thr-Glu-X32-Gly-Ser-X35-Thr-X37 wherein X1 is selected from the group consisting of Arg, Lys and Glu; X3 is selected from the group consisting of Gly, Gln and Pro; X4 is selected from the group consisting of Thr and Glu; X5 is selected from the group consisting of Ala and Leu; X6 is selected from the group consisting of Thr and Ser; X10 is selected from the group consisting of Glu and Gln; X14 is selected from the group consisting of Aad, His, Asp, Asn and Arg; X17 is selected from the group consisting of Gln, His and Thr; X19-X20 is selected from Ser-Ser, Thr-Thr, Ala-Thr, Ala-Ala, Gly-Thr, Gly-Gly and Ala-Asn or is absent; X27 is selected from the group consisting of Leu and Pro; X32 is selected from the group consisting of Val and Thr; X35 is selected from the group consisting of Asn and Ser; X37 is selected from the group consisting of Hyp and Pro; and X2 and X7 are amino acid residues whose side chains together form a lactam bridge, wherein: X2 is Asp and X7 is Lys; X2 is Asp and X7 is Orn; X2 is Asp and X7 is Dab; X2 is Asp and X7 is hLys; X2 is Dap and X7 is Aad; X2 is Glu and X7 is Dab; or X2 is Dab and X7 is Glu; or a pharmaceutically acceptable salt or solvate thereof. R 1 is hydrogen, C 1-4 acyl, benzoyl or C 1-4 alkyl, or a half-life extending moiety M, wherein M is optionally linked to Z via a linker moiety L; R 2 is OH or NHR 3, wherein R 3 is hydrogen or C 1-3 -alkyl; and Z is an amino acid sequence of formula I: X1-X2-X3-X4-X5-X6-X7-Ala-Thr-X10-Arg-Leu-Ala-X14-Phe-Leu-X17-Arg-X19-X20-Phe-Gly(Me)-Ala-Ile(Me)-X27-Ser-Ser-Thr-Glu-X32-Gly-Ser-X35-Thr-X37 wherein X1 is selected from the group consisting of Arg, Lys and Glu; X3 is selected from the group consisting of Gly, Gln and Pro; X4 is selected from the group consisting of Thr and Glu; X5 is selected from the group consisting of Ala and Leu; X6 is selected from the group consisting of Thr and Ser; X10 is selected from the group consisting of Glu and Gln; X14 is selected from the group consisting of Aad, His, Asp, Asn and Arg; X17 is selected from the group consisting of Gln, His and Thr; X19-X20 is selected from Ser-Ser, Thr-Thr, Ala-Thr, Ala-Ala, Gly-Thr, Gly-Gly and Ala-Asn or is absent; X27 is selected from the group consisting of Leu and Pro; X32 is selected from the group consisting of Val and Thr; X35 is selected from the group consisting of Asn and Ser; X37 is selected from the group consisting of Hyp and Pro; and X2 and X7 are amino acid residues whose side chains together form a lactam bridge, wherein: X2 is Asp and X7 is Lys; X2 is Asp and X7 is Orn; X2 is Asp and X7 is Dab; X2 is Asp and X7 is hLys; X2 is Dap and X7 is Aad; X2 is Glu and X7 is Dab; or X2 is Dab and X7 is Glu; X1 is selected from the group consisting of Arg, Lys and Glu; X3 is selected from the group consisting of Gly, Gln and Pro; X4 is selected from the group consisting of Thr and Glu; X5 is selected from the group consisting of Ala and Leu; X6 is selected from the group consisting of Thr and Ser; X10 is selected from the group consisting of Glu and Gln; X14 is selected from the group consisting of Aad, His, Asp, Asn and Arg; X17 is selected from the group consisting of Gln, His and Thr; X19-X20 is selected from Ser-Ser, Thr-Thr, Ala-Thr, Ala-Ala, Gly-Thr, Gly-Gly and Ala-Asn or is absent; X27 is selected from the group consisting of Leu and Pro; X32 is selected from the group consisting of Val and Thr; X35 is selected from the group consisting of Asn and Ser; X37 is selected from the group consisting of Hyp and Pro; and X2 and X7 are amino acid residues whose side chains together form a lactam bridge, wherein: X2 is Asp and X7 is Lys; X2 is Asp and X7 is Orn; X2 is Asp and X7 is Dab; X2 is Asp and X7 is hLys; X2 is Dap and X7 is Aad; X2 is Glu and X7 is Dab; or X2 is Dab and X7 is Glu; or a pharmaceutically acceptable salt or solvate thereof.