  We introduce a system of parameters for the Monte Carlo generation of Lorentz
invariant phase space that is particularly well-suited to the treatment of the
infrared divergences that occur in the most singular, Born-like configurations
of $1\to n$ QCD processes. A key feature is that particle momenta are generated
independently of one another, leading to a simple parameterisation of all such
IR limits. We exemplify the use of these variables in conjunction with the
projection to Born subtraction technique at next-to-next-to-leading order. The
geometric origins of this parameterisation lie in a coordinate chart on a
Grassmannian manifold.
