We develop an approach to estimate and characterize trace gas retrievals in the presence of clouds in high spectral measurements of upwelling radiance in the infrared spectral region (650--2260 cm-1). The radiance contribution of clouds is parameterized in terms of a set of frequency-dependent nonscattering optical depths and a cloud height. These cloud parameters are retrieved jointly with surface temperature, emissivity, atmospheric temperature, and trace gases such as ozone from spectral data. We demonstrate the application of this approach using data from the Tropospheric Emission Spectrometer (TES) and test data simulated with a scattering radiative transfer model. We show the value of this approach in that it results in accurate estimates of errors for trace gas retrievals, and the retrieved values improve over the initial guess for a wide range of cloud conditions. Comparisons are made between TES retrievals of ozone, temperature, and water to model fields from the Global Modeling and Assimilation Office (GMAO), temperature retrievals from the Atmospheric Infrared Sounder (AIRS), tropospheric ozone columns from the Goddard Earth Observing System (GEOS) GEOS-Chem, and ozone retrievals from the Total Ozone Mapping Spectrometer (TOMS). In each of these cases, this cloud retrieval approach does not introduce observable biases into TES retrievals.