Cohen has reported a negative correlation between lung cancer mortality and average radon levels by county. In this paper, the correlation of U.S. county mortality rates for various types of cancers during the period 1970-1994 with Cohen's radon measurements is examined. In general, quantitatively similar, strongly negative correlations are found for cancers strongly linked to cigarette smoking, weaker negative correlations are found for cancers moderately increased by smoking, whereas no such correlation is found for cancers not linked to smoking. The results indicate that the negative trend previously reported for lung cancer can be largely accounted for by a negative correlation between smoking and radon levels across counties. Hence, the observed ecological correlation provides no substantial evidence for a protective effect of low level radon exposure.