The rapid proliferation of cell phone use and the accompanying decline in landline service in recent years have resulted in substantial potential for coverage bias in landline random-digit-dial telephone surveys, which has led to the implementation of dual-frame designs that incorporate both landline and cell phone samples. Consequently, researchers have developed methods to allocate samples and combine the data from the two frames. In this article, we review point and interval estimation methods of proportions that can be used to analyze overlapping dual-frame surveys. We use data from the survey of attitudes toward immigrants and immigration (Opinions and Attitudes of the Andalusian Population regarding Immigration survey), a dual-frame telephone survey conducted in Andalusia, Spain, to explore these different statistical adjustments for combining landline and cell phone samples. Our application obtains good results for calibration, fixed weight, pseudo-empirical likelihood, and single-frame procedures. We recommend that one of these internally consistent estimators be used in practice. The results of these methods of estimation show that the negative image toward immigration continues to spread.