With declining response rates, dealing with non-response has become more costly and time-intensive. One practical approach is to carry out non-response follow-up on only a portion of the sample, such as by limiting computer-assisted telephone interviewing (CATI) to a random subsample. This is a generalization of the classical approach described by Hansen and Hurwitz (1946). The Canadian Social Survey experimented with this approach and restricted CATI operations on two iterations of the survey. This presentation covers the adjustments that were applied to the weights of responding units to adjust for this subsampling. Moreover, it presents alternate estimators that could be used, their theoretical properties with respect to biasedness, and the results of a simulation study comparing these estimators.