In estimating the total of a finite population the minimum variance estimate in a given class of linear unbiased estimates depends on the population values. In such a situation, the criterion of the ‘necessary best estimate’ is proposed by Ajgaonkar [1], in order to choose a serviceable estimate purely from practical point of view; and it was proved by him that in a particular subclass T5of linear estimates of the population total, the well known Horvitz-Thomson estimate, is the ‘necessary best estimate’ in sampling with varying probabilities without replacement. In this paper the result is generalized to the class of all linear estimates of the population total and for any sampling design.