This paper addresses the issue of finding the most efficient estimator of the normal population mean when the population “Coefficient of Variation (C. V.)” is ‘Rather-Very-Large’ though unknown, using a small sample (sample-size ≤ 30). The paper proposes an “Efficient Iterative Estimation Algorithm exploiting sample “C. V.” for an efficient Normal Mean estimation”. The MSEs of the estimators per this strategy have very intricate algebraic expression depending on the unknown values of population parameters, and hence are not amenable to an analytical study determining the extent of gain in their relative efficiencies with respect to the Usual Unbiased Estimator X ̅(sample mean ~ Say ‘UUE’). Nevertheless, we examine these relative efficiencies of our estimators with respect to the Usual Unbiased Estimator, by means of an illustrative simulation empirical study. MATLAB 220.127.116.111 (R2008b) is used in programming this illustrative ‘Simulated Empirical Numerical Study’.