Using 960 brown laying hens from 20 to 48 wk of age, in a 4 × 5 factorial arrangement, the effects on production, quality of eggs, and nutrient balance of analysed 18, 41, 61, and 111 mg kg^-1 of copper (Cu) and of 0.550%, 0.679%, 0.793%, 0.845%, and 0.948% of methionine and cysteine (Met + Cys) were evaluated. Treatments were administered to six replicate cages (eight hens per cage). At the 49th wk of age, 320 of these hens were kept under the same experimental conditions to evaluate the nutrient balance, and each treatment was allocated to four replicate cages (four hens per cage). The trend of interaction effect between Cu and Met + Cys levels was observed on egg weight and mass. The interaction between mineral and amino acid was characterized on egg quality variables. Quadratic equations indicated that increasing the dietary level of Cu reduced the estimate requirement of Met + Cys for hens. Across the entire experimental period, the total estimated Met + Cys level was 0.755% ± 0.021% based on the performance variables. As Cu increased in the diet, it decreased the estimated Met + Cys level to ensure egg weight, mass, and egg quality. Level of chelated Cu above 23 mg kg^-1 may negatively affect the egg quality.