The invention relates to a cosmetic mixture for the oxidation tinting of keratin fibres, containing in a support material suitable for tinting keratin fibres (a) at least one laccase-type enzyme; (b) at least one polymer thickener selected from the group constituted by: (i) amphiphilic non-ionic polymers comprising at least one fatty chain and at least one hydrophilic unit; (ii) anionic amphiphilic polymers comprising at least one hydrophilic unit and at least one fatty chain unit; (iii) cross-linked acrylic acid homopolymers; (iv) cross-linked 2-acrylamide-2-methyl-propane sulfonic acid homopolymers and their cross-linked acrylamide copolymers, which are partially or fully neutralized; (v) ammonium acrylate homopolymers or ammonium acrylate and acrylamide copolymers; (vi) dimethylaminoethyl-methacrylate homopolymers quatemized by methyl chloride or dimethylaminoethyl-methacrylate copolymers quaternized by methyl chloride and acrylamide copolymers; (vii) non-ionic guar gums; (viii) scleroglucan gum (a biopolysaccharide of microbial origin): (ix) gums made of vegetable exudates such as gum arabic, gum ghatti, gum karaya and gum tragacanth; and (c) at least one oxidation tint. The invention also relates to the tinting methods making use of the above mixture.