In one embodiment, a method is provided for incremental routing of a circuit design having modified and unmodified signals. Critical routed signals of the partially routed circuit design are determined. For each critical routed signal, a first set of routing constraints is applied to prevent rerouting of the signal. The partially routed circuit design is routed according to the first set of routing constraints to produce a non-conflicting routing solution. In response to the non-conflicting routing solution not meeting timing requirements, the first set of routing constraints is removed and post-routing optimization processes are performed on the non-conflicting routing solution to reduce propagation delay of one or more signals.