  For the case of $n$-jet production at next-to-next-to-leading order in the
QCD coupling, in the infrared divergent corners of phase space where particles
are collinear or soft, one must evaluate $(n+1)$-parton final-state one-loop
amplitudes through $\Ord(\eps^2)$, where $\eps$ is the dimensional
regularization parameter. For the case of gluons, we present to all orders in
$\eps$ the required universal functions which describe the behavior of one-loop
amplitudes in the soft and collinear regions of phase space. An explicit
example is discussed for three-parton production in multi-Regge kinematics that
has applications to the next-to-leading logarithmic corrections to the BFKL
equation.
