We study consistent network updates with the focus on min-imizing transient congestion. While we migrate the network from its ini-tial configuration to its final configuration, we allow each flow to split itsdata between the old and the new path. The goal is to find a sequenceof at most n split ratios for each flow that allows it to transition to thefinal configuration while minimizing congestion. We study the computa-tional complexity of different variants of this problem, and we find thatthe most general variant of our problem can be solved in polynomialtime, and we show how to reduce it to a linear programming problem.While most literature that studies congestion-free updates simply find asolution that is good enough, our model is capable of finding an opti-mal solution that minimizes the maximum link utilization. In order toimprove the scalability of our approach, we propose multiple techniques,and we run experiments which show that these techniques can improvecomputation time by an order of magnitude.