The edge method is a widely used way to assess the on-orbit Modulation Transfer Function (MTF). Since good quality is required for the edge, the higher the spatial resolution, the better the results are. In this case, an artificial target can be built and used to ensure a good edge quality. For moderate spatial resolutions, only natural targets are available. Hence the edge quality is unknown and generally rather poor. Improvements of the method have been researched in order to compensate for the poor quality of natural edges. This has been done through the use of symmetry and/or a transfer function model, which enables the elimination of noise. This has also been used for artificial target. In this case, the use of the model overcomes the incomplete sampling when the target is too small or gives the opportunity to assess the defocus of the sensor. This paper begins with a recall of the method followed by a presentation of the changes relying on transfer function parametric model. The transfer function model and the process corresponding to the changes are described. Applications of these changes for several satellites of the French spatial agency are presented: for SPOT 1, it enables to assess XS MTF with natural edges, for SPOT 5, it enables to use the Salon-de-Provence artificial target for MTF assessment in the HM mode, and for the foreseen Pleiades, it enables to estimate the defocus.