The invention concerns a process to manufacture a flat-rolled product, notably for the aeronautic industry containing aluminum alloy comprising 2.1% to 3.9% Cu by weight, 0.7% to 2.0% Li by weight, 0.1% to 1,0% Mg by weight, 0% to 0.6% Ag by weight, 0% to 1% Zn by weight, at least 0.20% Fe +Si by weight, at least one element chosen from Zr, Mn, Cr, Sc, Hf and Ti, the quantity of said element, if chosen, being 0.05% to 0.18% by weight for Zn, 0.1% to 0.6% by weight for Mn, 0.05% to 0.3% by weight for Cr, 0.02% to 0.2% by weight for Sc, 0.05% to 0.5% by weight for Hf and 0.01% to 0.15% by weight for Ti, the other elements at most 0.05% by weight each and 0.15% by weight in total, the rest being aluminum, in which, notably a flattening and/or stretching is performed with a cumulated deformation of at least 0.5% and less than 3%, and a short heat-treatment is performed in which the sheet reaches a temperature between 130° C. and 170° C. for a period of 0.1 to 13 hours. The invention notably makes it possible to simplify the forming process of fuselage skins and to improve the balance between static mechanical strength properties and damage tolerance properties.