The tropical tropopause, a transition layer between the troposphere and stratosphere, is important for global climate and atmospheric chemistry. Several studies have reported multi-decadal tropical tropopause cooling and have suggested a correlation between observed tropopause temperature and stratospheric water vapor. Water vapor changes have in turn been linked to changes in surface warming rates. Our more rigorous and thorough examination of the observations on which trend estimates are based, especially at the tropopause, shows these trends have greater uncertainty than previously suggested and the cooling may not even be statistically significant. We used two approaches to adjust cold-point tropopause (the point of minimum temperature in a vertical profile) trends based on radiosonde observations for time-varying biases. Our results are consistent with expectations based on a conceptual model of tropopause changes and could resolve discrepancies between complex climate models and observations