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The BEIR-VI Report suggests that the large discrepancy between the observed lung cancer rate vs. radon exposure relationship for U.S. counties, and the predictions of linear no-threshold theory, may be explained by a strong negative correlation between smoking intensity and radon exposure. It proposes a model for testing that suggestion. We apply that model to the detailed data for U.S. counties; analysis shows that even a perfect negative correlation explains little more than half of the discrepancy, and the largest not-implausible correlation can explain less than a quarter of the discrepancy. We then extend the BEIR-VI suggestion to include a strong negative correlation between both the prevalence of smoking and the intensity of smoking. The largest not-implausible correlations can explain no more than 30% of the discrepancy. It is concluded that the previous interpretation of these data, that linear no-threshold theory fails this test, is sustained.