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Due to its high variability and adaptability to different regions, the Eucalyptus species are planted in the whole world. This work aimed to verify the efficiency of the selection indices, in a population of Eucalyptus grandis. The classic index Hazel (1943) and Smith (1936) and the index based on the desired profits had been used (PESEK & BAKER, 1969), besides the indices base (WILLIANS, 1962), free of weights and parameters (ELSTON, 1963) and the based one on the addition of Ranks (MULAMBA & MOCK, 1978). The direct and indirect selections had not been efficient; therefore they had not gotten the distribution of profits desired. The selection indices had not been efficient in the direction of getting a balanced profit distribution, in accordance to the objectives of the work. The Free Index of Weights and Parameters (ELSTON, 1963) presented waited balanced answers, in accordance to the aims of this work.