Adaptive cluster sampling (ACS) has been a very important tool in estimation of population parameters of rare and clustered population. The fundamental idea behind this sampling plan is to decide on an initial sample from a defined population and to keep on sampling within the vicinity of the units that satisfy the condition that at least one characteristic of interest exists in a unit selected in the initial sample. Despite being an important tool for sampling rare and clustered population, adaptive cluster sampling design is unable to control the final sample size when no prior knowledge of the population is available. Thus adaptive cluster sampling with data-driven stopping rule (ACS’) was proposed to control the final sample size when prior knowledge of population structure is not available. This study examined the behavior of the HT, and HH estimator under the ACS design and ACS’ design using artificial population that is designed to have all the characteristics of a rare and clustered population. The efficiencies of the HT and HH estimator were used to determine the most efficient design in estimation of population mean in rare and clustered population. Results of both the simulated data and the real data show that the adaptive cluster sampling with stopping rule is more efficient for estimation of rare and clustered population than ordinary adaptive cluster sampling.