Abstract In sample surveys the ratio (product) method of estimation is quite effective when there is a positively (negatively) high correlation between the study variate and an auxiliary variate on which supplementary information is available. This paper considers four estimators suited for cases where these correlations are only moderate and gives a rule of thumb for choosing among these and the traditional estimators. Such a choice needs a good guess of the interval containing a certain parameterk, which may not be hard in survey practice. A numerical example has been included for the case of positive correlation for illustration. An extension for using multiauxiliary information is also considere