Recently, an analytical-numerical solution to dipole-field diffraction by an impedance wedge has been reported and a uniform asymptotic solution for the related space waves in the far field is given in [1, 2]. Additional wave ingredients, however, can be generated, like surface waves excited by the dipole itself on the wedge's face close to the dipole, the diffraction, reflection and transmission of these surface waves at the edge, as well as surface waves excited by the incident space wave at the edge of the wedge. This paper studies these waves and presents their non-uniform asymptotic formulae.