A process for the manufacture of a composite structure includes the following stages: a) providing a donor substrate comprising a first surface and a support substrate; b) forming a zone of weakening in the donor substrate, the zone of weakening delimiting, with the first surface of the donor substrate, a working layer; c) assembling the support substrate and the donor substrate; d) fracturing the donor substrate along the zone of weakening; and e) thinning the working layer so as to form a thinned working layer. Stage b) is carried out so that the working layer exhibits a thickness profile appropriate for compensating for the nonuniformity in consumption of the working layer during stage e).