Cut-off sampling has been widely used for a highly skewed population like a business survey by discarding a part of the population, so called a take-nothing stratum. For a more accurate estimate of the population total, Hwang and Shin (2013) suggested a composite estimator of a take-nothing stratum total that combined the survey results of a take-nothing stratum and a take-some sub-stratum (a part of take-some stratum). In this paper we propose a new cut-off sampling scheme by considering a cost function and a composite estimator based on the proposed sampling scheme. Small simulation studies compared the performances of known composite estimators and the new composite estimator suggested in this study. We also use Briquette Consumption Survey data for real data analysis.