We present a new method for solving the BFKL evolution applicable at both leading and next-to-leading logarithmic accuracy, and tailored to the study of QCD multijet events at colliders. We utilise this to discuss corrections to the standard analysis. There are known, large corrections from energy and momentum conservation. We show that, despite claims to the contrary in the literature, these are unrelated to the next-to-leading logarithmic corrections to the evolution kernel.