We consider the problem of admission control to a multiserver finite buffer queue under partial information+ The controller cannot see the queue but is informed immediately if an admitted customer is lost due to buffer overflow+ Turning away~i+e+, blocking! customers is costly and so is losing an admitted customer+ The latter cost is greater than that of blocking+ The controller's objective is to minimize the average cost of blocking and rejection per incoming customer+ Lin and Ross @11# studied this problem for multiserver loss systems+ We extend their work by allowing a finite buffer and the arrival process to be of the renewal type+ We propose a control policy based on a novel state aggregation approach that exploits the regenerative structure of the system, performs well, and gives a lower bound on the optimal cost+ The control policy is inspired by a simulation technique that reduces the variance of the estimators by not simulating the customer service process+ Numerical experiments show that our bound varies with the load offered to the system and is typically within 1% and 10% of the optimal cost+ Also, our bound is tight in the important case when the cost of blocking is low compared to the cost of rejection and the load offered to the system is high+ The quality of the bound degrades with the degree of state aggregation, but the computational effort is comparatively small+ Moreover, the control policies that we obtain perform better compared to a heuristic suggested by Lin and Ross+ The state aggregation technique developed in this article can be used more generally to solve problems in which the objective is to