Satellite-borne radiometers have been used with increasing success to monitor geophysical parameters. The majority of the statistical retrieval schemes currently in use for estimating atmospheric temperature profiles are one-dimensional (1-D), that is, they consider correlations only in the dimension perpendicular to the surface. Here, a two-dimensional (2-D) spatial filter, optimum in the minimum-mean-square error sense, is used to retrieve atmospheric temperature profiles from Microwave Sounder Unit measurements. Horizontal correlations along the orbital track are taken into account. This additional statistical information results in lower mean-square errors for the 2-D filter compared to that of its 1-D counterpart. The previously unstudied behavior of retrieval errors as a function of spatial frequency along the orbital track is also investigated. A large part of the improved performance of the 2-D filter is due to the reduction of short spatial wavelength components in the error. In addition, retrievals were carded out over a severe cold front. The 2-D technique yielded substantially lower errors than the 1-D approach. The latter does not perform so well over fronts because of the loss in vertical correlation due to the presence of layers of air with different lapse rates.