We present global, vertical profile estimates of the HDO/H2O ratio from the Tropospheric Emission Spectrometer (TES) on the Earth Observing System (EOS) Aura satellite. We emphasize in this paper the estimation approach and error characterization, which are critical to determining the very small absolute concentration of HDO relative to H2O and its uncertainty. These estimates were made from TES nadir-viewing (downlooking) thermal infrared spectral radiances observed on 20 September 2004. Profiles of HDO and H2O are simultaneously estimated from the observed radiances and a profile of the ratio is then calculated. This simultaneous, or "joint," estimate is regularized with an a priori covariance matrix that includes expected correlations between HDO and H2O. This approach minimizes errors in the profile of the HDO/H2O ratio that are due to overlapping HDO and H2O spectroscopic lines. Under clear-sky conditions in the tropics, TES estimates of the HDO/H2O ratio are sensitive to the distribution of the actual ratio between the surface and about 300 hPa with peak sensitivity at 700 hPa. The sensitivity decreases with latitude through its dependence on temperature and water amount. We estimate a precision of approximately 1% to 2% for the ratio of the HDO/H2O tropospheric densities; however, there is possibly a bias of approximately 5% in the ratio due to the HDO spectroscopic line strengths. These global observations clearly show increased isotopic depletion of water vapor at higher latitudes as well as increased depletion in the upper troposphere versus the lower troposphere.