Trace-element concentrations in baseline samples from a survey of aquifers used as potable-water supplies in the United States are summarized using methods appropriate for data with multiple detection limits. The resulting statistical distribution models are used to develop summary statistics and estimate probabilities of exceeding water-quality standards. The models are based on data from the major aquifer studies of the USGS National Water Quality Assessment (NAWQA) Program. These data were produced with a nationally-consistent sampling and analytical framework specifically designed to determine the quality of the most important potable groundwater resources during the years 1991-2001. The analytical data for all elements surveyed contain values that were below several detection limits. Such datasets are referred to as multiply-censored data. To address this issue, a robust semi-parametric statistical method called regression on order statistics (ROS) is employed. Utilizing the 90th-95th percentile as an arbitrary range for the upper limits of expected baseline concentrations, the models show that baseline concentrations of dissolved Ba and Zn are below 500 ??g/L. For the same percentile range, dissolved As, Cu and Mo concentrations are below 10 ??g/L, and dissolved Ag, Be, Cd, Co, Cr, Ni, Pb, Sb and Se are below 1-5 ??g/L. These models are also used to determine the probabilities that potable ground waters exceed drinking water standards. For dissolved Ba, Cr, Cu, Pb, Ni, Mo and Se, the likelihood of exceeding the US Environmental Protection Agency standards at the well-head is less than 1-1.5%. A notable exception is As, which has approximately a 7% chance of exceeding the maximum contaminant level (10 ??g/L) at the well head.