The use of several high-frequency, asymptotic techniques is explored for modeling the scattering, using higher-order diffractions, of radar targets composed of two or more parallel edges with diminishing electrical separation between them. The Uniform Theory of Diffraction (UTD) is one of the most popular and easily applied techniques; however, difficulties in accurately modeling second-order diffractions are inherent in the method due to the failure of the technique in overlapping transition regions. The effectiveness of the UTD, as the electrical size of the target decreases, is explored using a square cylinder. Other high-frequency methods for dealing with fields in overlapping transition regions are reviewed. Particularly, the Extended Spectral Theory of Diffraction (ESTD) and the Extended Physical Theory of Diffraction (EPTD) are examined, and the EPTD is applied to the scattering by a strip. Results are compared with UTD and moment method (MM) data. A hybrid method, using the UTD plus the ESTD or the EPTD, is recommended for accurately predicting the scattering of radar targets, even of small electrical size, at all observation angles.