We propose a snap-stabilizingk-wave algorithm for routed trees, called kWA, which implements k consecutive waves, k > 1. A snap-stabilizing algorithm, starting from an arbitrary system configuration, always behaves according to its specification. The maximum number of states per process is 2k + 1, better than the previous result of at most 3k states per process. A snap-stabilizing algorithm guarantees that, starting from an arbitrary system configuration, always behaves according to its specification.