I will present the approach to NNLO matching taken in VINCIA, which is based on nested phase-space generation with full 2nd-order matrix-element corrections. The method exploits a shower-style algorithm which differs from conventional ones in several ways, notably sectorized phase spaces and the inclusion of 2->4 branchings to cover parts of the double-soft and triple-collinear phase-space regions. This leads to several benefits, including matching the NNLO singularity structure point by point in phase space, high efficiency due to the absence of negative weights, and an expectation of small matching systematics as there is no dependence on any external resummations or auxiliary scales. Proofs of concept have so far been carried out for 2-body decays of colour singlets, but the general methodology should be extendable to hadron collisions, and to matching at N3LO.