  Yang-Mills tree-level amplitudes contain singularities of codimension one
like collinear and multi-particle factorizations, codimension two such as soft
limits, as well as higher codimension singularities. Traditionally, BCFW-like
deformations with one complex variable were used to explore collinear and
multi-particle channels. Higher codimension singularities need more complex
variables to be reached. In this paper, along with a discussion on higher
singularities and the role of the global residue theorem in this analysis, we
specifically consider soft singularities. This is done by extending Risager's
deformation to a $\mathbb C^2$-plane, i.e., two complex variables. The
two-complex-dimensional deformation is then used to recursively construct
Yang-Mills tree amplitudes.
