A method of producing a tire mix, including a first mixing step, in which a mix contains at least one cross-linkable unsaturated-chain polymer base, 10 to 100 phr of silica, and 1 to 20 phr of a silane bonding agent in the trialkoxymercaptoalkyl-silane class; and a final mixing step, in which a curing system is added to the mix. The silane bonding agent is used in adsorbed form on 0.5 to 2 phr of zinc oxide, and on 5 to 15 phr of carbon black. At the first mixing step, the mix contains 1 to 5 phr of one or more fatty acid derivatives, and, at the final mixing step, 1 to 2 phr of zinc oxide is added to the mix. The fatty acid derivatives are derived from condensation of a fatty acid, having a carbon number of 16 to 20, with an alcohol having a carbon number of 2 to 6, or with a primary or secondary amine having a carbon number of 2 to 6.