Atmospheric water-vapor isotopes have been proposed as a potentially powerful constraint on convection, which plays a critical role in Earth's present and future climate. It is shown here, however, that the mean tropical profile of HDO in the free troposphere does not usefully constrain the mean convective entrainment rate or precipitation efficiency. This is demonstrated using a single-column analytical model of atmospheric water isotopes. The model has three parameters: the entrainment rate, the precipitation efficiency, and the distance that evaporating condensates fall. At a given relative humidity, the possible range of HDO is small: its range is comparable to both the measurement uncertainty in the mean tropical profile and the structural uncertainty of a single-column model. Therefore, the mean tropical HDO profile is unlikely to add information about convective processes in a bulk-plume framework that cannot already be learned from relative humidity alone.