A cosmetic composition for the first stage of a permanent deformation of the hair contains, in a cosmetically acceptable vehicle, as a reducing agent, an amino mercaptoalkylamide having the formula ##STR1## wherein A represents the divalent radical, --(CH.sub.2).sub.n -- wherein n is a whole number ranging from 2 to 5, or the divalent radical --(CH.sub.2)--O--(CH.sub.2).sub.2 --, m is 0 or a whole number ranging from 1 to 4, and (i) when m is 0, R.sub.2 represents hydrogen methyl, ethyl, isopropyl, isobutyl, 2-methyl butyl, benzyl, 4-amino butyl, 3-guanidino propyl, 2-methylthio ethyl, carboxymethyl or 2-carboxyethyl, and (ii) when m is a whole number from 1 to 4, R.sub.1 represents hydrogen or lower alkyl having 1-5 carbon atoms, and the salts of the compound of formula I.

This invention provides compositions and methods for reducing odors associated with permanent hair waving by contacting the hair with a disulfide before, during, or after application of a sulfur-based reducing agent.