The simplicity and wide application of Greenberg et al. (1971) prompts to propose a set of alternative estimators of population total for multi-character surveys that elicit simultaneous information on many. sensitive study variables. The proposed estimators take into account the already known rough value of the correlation coefficient between Y(the characteristic under study) and p(the measure of size). These estimators are biased, but it is expected that the extent of bias will be smaller, since the proposed estimators are suitable for situations in between those optimum for the usual estimators and the estimators based on multi-characters for no correlation. The relative efficiency of the proposed estimators has been studied under a super population model through empirical study. It has been found through simulation study that a choice of an unrelated variable in the Greenberg et al. (1971) model could be made based on its correlation with the auxiliary variable used at estimation stage in multi-character surveys.