Abstract Two methods are employed to estimate the association of hydrocarbons, sulfur compounds, nitrogen compounds, natural ionizing radiation, and cigarette smoking with some age stratified and disease specific United States mortality rates for white males. The first method is based on a ridge regression technique and the second on a sign constrained least squares analysis. The measure of association between these environmental factors and mortality are quantified as elasticities; i.e., the indicated percentage change in the average mortality rate corresponding to a 1 % change in the average level of the environmental factor. Elasticities are estimated for age specific and disease specific mortality rates, and these values are then aggregated and compared to estimates corresponding to total mortality rates. Overall, consistent results are obtained using the above methods for sulfur compounds and cigarette smoking. Many of these results differ considerably from corresponding results obtained from the ordinary least squares regression analysis, highlighting the need for applying the appropriate estimation methods. In addition to the variables already specified, these analyses take into consideration the following groups of explanatory variables: • Climate — Precipitation, January temperature, July temperature, humidity, and solar radiation. • Socioeconomic — Age, education, sound housing, population per household, population density, % non-white, % white-collar, income, and city size.