Suppose we have independent random samples of sizesmandnrespectively from two populations characterized by a common location parameterθand unknown scale parameters. Letψxandψybe odd location estimators ofθbased on individual samples. Cohen (1976) suggested a combined estimatorδa, which under mild conditions on the density, is unbiased and improvesψxfor all a such that 0 <a≤a*(m, n), wherea*(m, n) is a constant andm, ndenote the two sample sizes. Bhattacharya (1981) enlarged this class by finding a larger upperboundA(m, n) for ‘a’. In this paper, we further improveA(m, n) and establish dominance ofδ1, over bothψxandψyin cases where Bhattacharya's bound does not help. We also consider, an unbiased estimator different fromδa, and determine conditions oncto improve bothψxandψy. Our results also take into account the cases not covered by Akai (1982).