The upper troposphere/lower stratosphere (UTLS) region plays an important role in the climate system. Changes in the structure and chemical composition of this region result in particularly large changes in radiative forcings of the atmosphere. Quantifying the processes that control UTLS composition (e.g., stratosphere-troposphere exchange) therefore represents a crucial task. We assess the influence of uncertainties in the atmospheric mixing strength on global UTLS distributions of greenhouse gases (water vapor, ozone, methane, and nitrous oxide) and associated radiative effects. The study is based on multiannual simulations with the Chemical Lagrangian Model of the Stratosphere (CLaMS) driven by ERA-Interim meteorological data and on a state-of-the-art radiance code. Mixing, the irreversible part of transport, is controlled by the local horizontal strain and vertical shear of the atmospheric flow. We find that simulated radiative effects of water vapor and ozone, both characterized by steep gradients in the UTLS, are particularly sensitive to uncertainties of the atmospheric mixing strength. Globally averaged radiative effects are about 0.72 and 0.17 W/m2 for water vapor and ozone, respectively. For ozone, the largest impact of mixing uncertainties is observed in the extra-tropical lower stratosphere.