Two alternate higher degree ratio-cum-product strategies viz. and are proposed for estimating population mean of the study variate Y utilising information on the auxiliary variate X. The proposed strategies, to first degree approximation, are as efficient as the conventional linear regression strategy in the optimum case. Further in the non optimum case also, the proposed strategies are superior to the corresponding ratio or product strategies as long as the difference between the weights used and optimum weights does not exceed certain specified value. It has also been established that the strategy could be preferred to the strategy under a simple and realisable condition. An attempt has also been made for making the strategy unbiased and the efficiency of the unbiased strategy his been studied.