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A commonly held view is that laboratory experiments provide researchers with more "control" than natural field experiments, and that this advantage is to be balanced against the disadvantage that laboratory experiments are less generalizable. This paper presents a simple model that explores circumstances under which natural field experiments provide researchers with more control than laboratory experiments afford. This stems from the covertness of natural field experiments: laboratory experiments provide researchers with a high degree of control in the environment which participants agree to be experimental subjects. When participants systematically opt out of laboratory experiments, the researcher's ability to manipulate certain variables is limited. In contrast, natural field experiments bypass the participation decision altogether and allow for a potentially more diverse participant pool within the market of interest. We show one particular case where such selection is invaluable: when treatment effects interact with participant characteristics.