A new asymptotic analysis of the high-frequency scattering by a pair of parallel wedges is presented, resulting in a uniform, closed-form approximation for the doubly diffracted field. The analysis is based on an extension of the physical theory of diffraction, in which the radiation integral over the actual induced currents is replaced by the Helmholtz integral over a surface enclosing the wedges. A term-by-term relationship is established between the geometrical theory of diffraction ray decomposition of the scattered field and the asymptotic decomposition of the radiation integral into endpoint contributions. The closed form expressions obtained for the various endpoint contributions to the singly diffracted field are used in an extended spectral theory of diffraction analysis of the doubly diffracted field to cast the latter in the form of a steepest descent path integral satisfying the principle of reciprocity. An Ansatz based on the uniform theory of diffraction in combination with a singularity-matching procedure is proposed to transform the initial nonuniform approximation for the doubly diffracted field into a uniform one. The latter includes terms to order k−1 and applies to all angles of incidence and scattering, including the overlapping transition regions. The limitations on this closed-form solution are that the incident wave be approximately plane throughout the gap between the edges, the observation point be in the far scattered field, and the gap be large in terms of the wavelength.