Historical information on changes in radiosonde instruments and observing methods is combined with time series of upper-air temperature data to estimate the effects of (1) changes in sensors, (2) changes in solar radiation corrections to the data, and (3) changes in the length of the train between the balloon and the instrument package. These changes can induce discontinuities in the temperature records from several tenths to as high as several degrees Celsius. The discontinuities can be larger than the temperature trends of a few tenths of a degree per decade, computed by previous investigators from radiosonde observations. An assessment of the 63-station network used by Angell to monitor tropospheric and stratospheric temperature suggests that about 43% of those stations' records have inhomogeneities, most notably in the stratosphere. These findings suggest that some previously computed temperature trends, especially estimates of stratospheric cooling, may be influenced by data inhomogeneities.