This paper analyses the impact of jitter when applied to route discovery in reactive (on-demand) routing protocols. In multi-hop non-synchronized wireless networks, jitter—a small, random variation in the timing of message emission—is commonly employed, as a means to avoid collisions of simultaneous transmissions by adjacent routers over the same channel. In a reactive routing protocol for sensor and ad hoc networks, jitter is recommended during the route discovery process, specifically, during the network-wide flooding of route request messages, in order to avoid collisions. Commonly, a simple uniform jitter is recommended. Alas, this is not without drawbacks: when applying uniform jitter to the route discovery process, an effect called delay inversion is observed. This paper, first, studies and quantifies this delay inversion effect. Second, this paper proposes an adaptive jitter mechanism, designed to alleviate the delay inversion effect and thereby to reduce the route discovery overhead and (ultimately) allow the routing protocol to find more optimal paths, as compared to uniform jitter. This paper presents both analytical and simulation studies, showing that the proposed adaptive jitter can effectively decrease the cost of route discovery and increase the path quality.