The precision of event-generator descriptions of collider final states plays an important role for both phenomenological and experimental applications. On the theoretical side, the challenge is to construct an explicit algorithmic solution to QFT with the highest precision possible. At LO, traditional strategies for combining matrix elements of different multiplicities with parton showers, like CKKW and MLM, come with a steep price tag in terms of additional computational power. At NLO, formalisms like POWHEG and MC@NLO have been limited to correcting a single partonic multiplicity at a time. I will discuss an alternative formalism, based on the paradigm of interleaved evolution, in which the perturbative series is cast as a single shower-like Markov chain, with coefficients that can be systematically upgraded at both LO and NLO, over all of phase space. The magnitude of the correction coefficients, in particular in the infrared limits, gives a powerful check on the "goodness" of different choices of shower evolution and renormalization-scale variables. The discussion will be limited to final-state showers, which is the only case that has so far been worked out in detail.
