In certain exponential life-testing models, the optimal number of replacements is a function of the unknown parameter which is being estimated. Two procedures are proposed in this paper to overcome this dificulty by sequentially estimating the parameter and redesigning the experiment in a model similar to that considered by Blight [1]. Monte Carlo studies indicate that such an approach yields results which are almost as good as the optimal design which depends on the unknown parameter. Life-test data on semiconductor devices is used for the purpose of illustrating the proposed procedures.