The application of a tapered resistive card to reduce the EM scattering from the edge of an impedance wedge is presented. The problem is two-dimensional, where the incident field is polarized transverse magnetic or electric to the axis of the wedge, and the resistive card is infinitesimally thin and is attached to the vertex of the wedge. An integral equation is formulated to solve for the scattering from the structure which utilizes a specialized Green's function for the impedance wedge. The integral equation is then solved using a method of moments technique. Since the presence of the wedge is taken into account by the Green's function, unknowns need to be placed only over the region of the resistive card and not along the boundaries of the wedge, thus reducing the size of the moment method matrix. Numerical optimization techniques are then employed to determine the resistance profiles for the cards which yield designs that minimize the scattered field over broad spatial regions and over broad frequency bands as well. The resulting designs for the resistive cards have therefore been optimized to yield maximum performance for scattering reduction. The application of this work to the reduction of edge diffraction from the edges of the ground plane of a microstrip antenna is also discussed, and measured as well as calculated results are presented.