To determine optimized dietary nutrient supply for common carp (Cyprinus carpio), nine isoenergetic diets were formulated according to a two-factorial central composite design on digestible basis. Digestible protein contents (DP) in diets ranged from 208.8 to 251.2 g/kg, and digestible fat-to-digestible carbohydrate energy ratios (DEF/DEC) varied from 0.79 to 1.21. Carp were fed four times a day at a daily feeding rate of 2.5 g/kg body weight for 56 days. Optima of responses were determined by applying the standard least squares method according to response surface methodology. All diets resulted in excellent performance with feed conversion ratios lower than 1 and digestible protein efficiency ratios (PER dig ) higher than 4.6. For most parameters, calculated extreme values were minimum points, except for FCR, retention efficiencies of digestible arginine (RetArg dig ) and of digestible methionine (RetMet dig ), being maximum points, and retention efficiencies of digestible isoleucine, digestible sulphuric amino acids and digestible lysine, being saddle points. Highest growth and feed utilization efficiency were graphically determined for a diet containing 208.8 g/kg DP/1.21 DEF/DEC. Body lipid was optically increased for 251.2 g/kg DP/0.79 DEF/DEC in comparison with 208.8 g/kg DP/1.21 DEF/DEC. K E Y W O R D Scarp, central composite design, digestible protein, energy, non-protein energy sources, response surface methodology