This paper examines trend uncertainties in layer-average free atmosphere temperatures arising from the use of different trend estimation methods. It also considers statistical issues that arise in assessing the significance of individual trends and of trend differences between data sets. Possible causes of these trends are not addressed. We use data from satellite and radiosonde measurements and from two reanalysis projects. To facilitate intercomparison, we compute from reanalyses and radiosonde data temperatures equivalent to those from the satellite-based Microwave Sounding Unit (MSU). We compare linear trends based on minimization of absolute deviations (LA) and minimization of squared deviations (LS). Differences are generally less than 0.05 ¿C/decade over 1959--1996. Over 1979--1993, they exceed 0.10 ¿C/decade for lower tropospheric time series and 0.15 ¿C/decade for the lower stratosphere. Trend fitting by the LA method can degrade the lower-tropospheric trend agreement of 0.03 ¿C/decade (over 1979--1996) previously reported for the MSU and radiosonde data. In assessing trend significance we employ two methods to account for temporal autocorrelation effects. With our preferred method, virtually none of the individual 1979--1993 trends in deep-layer temperatures are significantly different from zero. To examine trend differences between data sets we compute 95% confidence intervals for individual trends and show that these overlap for almost all data sets considered. Confidence intervals for lower-tropospheric trends encompass both zero and the model-projected trends due to anthropogenic effects. We also test the significance of a trend in d(t), the time series of differences between a pair of data sets. Use of d(t) removes variability common to both time series and facilitates identification of small trend differences. This more discerning test reveals that roughly 30% of the data set comparisons have significant differences in lower-tropospheric trends, primarily related to differences in measurement system. Our study gives empirical estimates of statistical uncertainties in recent atmospheric temperature trends. These estimates and the simple significance testing framework used here facilitate the interpretation of previous temperature trend comparisons involving satellite, radiosonde, and reanalysis data sets. ¿ 2000 American Geophysical Union