A compound that inhibits complement activation, comprising a peptide having a sequence: Xaa1 - Cys - Val - Xaa2 - Gln - Asp - Xaa3 - Gly - Xaa4 - His - Arg - Cys - Xaa5 (SEQ ID NO:26); wherein: Xaa1 is Ile, Val, Leu, Ac-Ile, Ac-Val, Ac-Leu or a dipeptide Gly-Ile; Xaa2 is Trp or an analog of Trp, wherein the analog of Trp has increased hydrophobic character as compared with Trp and is selected from (a) 5-fluoro- l -tryptophan, or 6-fluoro- l -tryptophan; or (b) 5-methoxytryptophan or 5-methyltryptophan; or (c) 1-methyltryptophan; with the proviso that, if X4aa3 is Trp, Xaa2 is the analog of Trp; Xaa3 is Trp or an analog of Trp having an indole hydrogen replaced with a fluorine atom, thereby increasing the hydrogen bond potential of the indole ring, optionally wherein the analog of Trp of Xaa3 is 5-fluoro- l -tryptophan, or 6-fluoro- l- tryptophan; Xaa4 is His, Ala, Phe or Trp, optionally wherein Xaa4 is Ala; Xaa5 is L-Thr, D-Thr, Ile, Val, Gly, a dipeptide Thr-Asn or Thr-Ala, or a tripeptide Thr-Ala-Asn, wherein a carboxy terminal -OH of any of the L-Thr, D-Thr, Ile, Val, Gly or Asn optionally is replaced by -NH2; and the two Cys residues are joined by a disulfide bond. Xaa1 - Cys - Val - Xaa2 - Gln - Asp - Xaa3 - Gly - Xaa4 - His - Arg - Cys - Xaa5 (SEQ ID NO:26); wherein: Xaa1 is Ile, Val, Leu, Ac-Ile, Ac-Val, Ac-Leu or a dipeptide Gly-Ile; Xaa2 is Trp or an analog of Trp, wherein the analog of Trp has increased hydrophobic character as compared with Trp and is selected from (a) 5-fluoro- l -tryptophan, or 6-fluoro- l -tryptophan; or (b) 5-methoxytryptophan or 5-methyltryptophan; or (c) 1-methyltryptophan; with the proviso that, if X4aa3 is Trp, Xaa2 is the analog of Trp; Xaa3 is Trp or an analog of Trp having an indole hydrogen replaced with a fluorine atom, thereby increasing the hydrogen bond potential of the indole ring, optionally wherein the analog of Trp of Xaa3 is 5-fluoro- l -tryptophan, or 6-fluoro- l- tryptophan; Xaa4 is His, Ala, Phe or Trp, optionally wherein Xaa4 is Ala; Xaa5 is L-Thr, D-Thr, Ile, Val, Gly, a dipeptide Thr-Asn or Thr-Ala, or a tripeptide Thr-Ala-Asn, wherein a carboxy terminal -OH of any of the L-Thr, D-Thr, Ile, Val, Gly or Asn optionally is replaced by -NH2; and Xaa1 is Ile, Val, Leu, Ac-Ile, Ac-Val, Ac-Leu or a dipeptide Gly-Ile; Xaa2 is Trp or an analog of Trp, wherein the analog of Trp has increased hydrophobic character as compared with Trp and is selected from (a) 5-fluoro- l -tryptophan, or 6-fluoro- l -tryptophan; or (b) 5-methoxytryptophan or 5-methyltryptophan; or (c) 1-methyltryptophan; with the proviso that, if X4aa3 is Trp, Xaa2 is the analog of Trp; (a) 5-fluoro- l -tryptophan, or 6-fluoro- l -tryptophan; or (b) 5-methoxytryptophan or 5-methyltryptophan; or (c) 1-methyltryptophan; Xaa3 is Trp or an analog of Trp having an indole hydrogen replaced with a fluorine atom, thereby increasing the hydrogen bond potential of the indole ring, optionally wherein the analog of Trp of Xaa3 is 5-fluoro- l -tryptophan, or 6-fluoro- l- tryptophan; Xaa4 is His, Ala, Phe or Trp, optionally wherein Xaa4 is Ala; Xaa5 is L-Thr, D-Thr, Ile, Val, Gly, a dipeptide Thr-Asn or Thr-Ala, or a tripeptide Thr-Ala-Asn, wherein a carboxy terminal -OH of any of the L-Thr, D-Thr, Ile, Val, Gly or Asn optionally is replaced by -NH2; and the two Cys residues are joined by a disulfide bond.