Under recent dramatic declines in response rates, various procedures have been considered among survey practitioners to reduce nonresponse in order to avoid its potential impairment to the inference. In the random digit dialing telephone surveys, substantial efforts are often required to obtain the initial contact for the screener interview. To reduce a burden with higher data collection costs, refusal conversion can be administered only to a random portion of the sample, reducing nonresponse (bias) with an expense of sample variability increment due to the associated weight adjustment. In this paper, we provide ways to determine the optimal subsampling rate using a linear cost model. Our approach for refusal subsampling is to predetermine a random portion from the full sample and to apply refusal conversion efforts if needed only to the subsample.