In this paper, we argue that enforcing routing consistency in keybased routing (KBR) protocols can simplify P2P application design and make structured P2P overlays suitable for more applications. We define two levels of routing consistency semantics, namely weakly consistent KBR and strongly consistent KBR. We focus on an algorithm that provides strong consistency based on group membership service and weakly consistent KBR. The algorithm provides a continuum of consistency levels for applications with a tunable parameter.