The problem of removal of collimation distortion due to employing a slit collimation system in small-angle X-ray scattering experiments is considered for anisotropic objects in general and for orientated macromolecules in particular. A mathematical statement of the problem is presented, and two approaches to `de-smear' the experimental scattering intensity are described. The first method seeks the theoretical scattering intensity as a linear combination of two-dimensional basis functions (B splines). The combination coefficients are found using the χ2and two-dimensional curvature-minimization criteria. The second approach is based on the iterative Friedman method, which was generalized to be effective for the problem of interest. The described methods are applied to simulated and experimental data, and the results are discussed.