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Three experiments were carried out to estimate the optimal ratios of digestible phenylalanine + tyrosine (Phe + Tyr), histidine (His), and leucine (Leu) relative to digestible lysine (Lys) for performance and carcass criteria of Cobb-500 broilers from 8 to 17 d of age. In each experiment, 160 male chicks were allocated to a completely randomized experimental design with eight replicate pens, each receiving five dietary treatments. A common, semi-purified basal diet was formulated to meet all dietary recommendations except for those of the tested amino acids (i.e., Phe + Tyr, His, and Leu). Growth performance and carcass characteristics data were analyzed using various requirement-estimation models, including 95% of the quadratic regression, linear response plateau (LRP; i.e., stepwise regression), LRP-to-quadratic regression ratio; and quadratic broken line (QBL). Graded digestible Phe + Tyr ratios elicited a quadratic response (P < 0.05) in body weight gain and linear responses (P < 0.05) in breast and breast fillet weights. Linear effects (P < 0.05) were also observed when graded ratios of digestible His were fed for feed intake and weight gain, and quadratic responses (P < 0.05) were noted for feed conversion ratio and breast and breast fillet weights and yields. Graded Leu ratios elicited quadratic responses (P < 0.05) in feed intake, weight gain, and breast and breast fillet weight and yield. Based on growth and carcass parameters, the estimated ideal digestible ratios of Phe + Tyr, His, and Leu relative to digestible Lys were 112, 38, and 104%, respectively, for broiler chicks raised from 8 to 17 d of age., (© The Author 2016. Published by Oxford University Press on behalf of Poultry Science Association.)