The tropical tropopause is a transition layer between the troposphere and stratosphere that influences global climate and atmospheric chemistry. Several studies have reported multidecadal tropical tropopause cooling and have suggested a correlation between observed tropopause temperature and stratospheric water vapor. Our more rigorous examination of the observations shows tropopause trends have greater uncertainty than previously suggested and the cooling may not be statistically significant. We used two approaches to remove time-varying bias effects from cold-point tropopause trends estimated from radiosonde observations. Our results are consistent with expectations from a conceptual model of tropopause changes and could resolve discrepancies between complex climate models and observations.