BACKGROUND: Hierarchical Bayesian methods have been used in previous papers to estimate national mean effects of air pollutants on daily deaths in time-series analyses. OBJECTIVES: To obtain maximum likelihood estimates of the common national effects of the criteria pollutants on mortality based on time-series data from up to 108 metropolitan areas in the U.S. METHODS: We used a subsampling bootstrap procedure to obtain the maximum likelihood estimates and confidence bounds for common national effects of the criteria pollutants, as measured by the percentage increase in daily mortality associated with a unit increase in daily 24-hour mean pollutant concentration on the previous day, while controlling weather and temporal trends. Five pollutants, PM10, ozone, CO, NO2, and SO2 were considered in single and multi-pollutant analyses. Flexible ambient concentration-response models for the pollutant effects were considered as well. Limited sensitivity analyses with different degrees of freedom for time trends were performed. RESULTS: In single pollutant models, we observed significant associations of daily deaths with all pollutants. The ozone coefficient was highly sensitive to the degree of smoothing of time trends. Among the gases, SO2 and NO2 were most strongly associated with mortality. The flexible ambient concentration-response curve for ozone showed evidence of non-linearity and a threshold at about 30 ppb. CONCLUSIONS: Differences between the results of our analyses and those reported from the Bayesian approach suggest that estimates of the quantitative impact of pollutants are dependent on choice of statistical approach, although results are not directly comparable because they are based on different data. Additionally, the estimate of the ozone-mortality coefficient depends on the amount of smoothing of time trends.