  This paper introduces a new method for constructing approximate solutions to
a class of Wiener--Hopf equations. This is particularly useful since exact
solutions of this class of Wiener--Hopf equations, at the moment, cannot be
obtained. The proposed method could be considered as a generalisation of the
pole removal technique. The error in the approximation can be explicitly
estimated, and by a sufficient number of iterations could be made arbitrary
small. Typically only a few iterations are required for practical purposes. The
theory is illustrated by numerical examples that demonstrate the advantages of
the proposed procedure. This method was motivated and successfully applied to
problems in acoustics.
