Cut-off sampling is widely used for a highly skewed population like a business survey by discarding a part of the population (the take-nothing stratum). In this paper, we suggest a new composite estimator of the take-nothing stratum total obtained by use of the survey results of the take-nothing stratum and a take-some sub-stratum (a part of take-some stratum) for a more accurate estimate of the population total. Small simulation studies are conducted to compare the performances of known estimators and the new composite estimator suggested in this study. In addition, we use briquette consumption survey data for real data analysis.