We study the scale-invariant O( g4) kernel which appears as an infra-red contribution in the BFKL evolution equation and is constructed via multiparticle t-channel unitarity. We detail the variety of Ward identity constraints and infra-red cancellations that characterize its infrared behaviour. We give an analytic form for the full non-forward kernel. For the forward kernel controlling parton evolution at small x, we give an impact parameter representation, derive the eigenvalue spectrum, and demonstrate a holomorphic factorisation property related to conformal invariance. The present results indicate that, at next-to-leading order, the transverse momentum infra-red region may produce a significant reduction of the BFKL small- x behavior.