Most of existing routing methods in wireless sensor networks to counter the local eavesdropping-based packet-tracing deal with a single asset and suffer from the packet-delivery latency as they prefer to take a separate path of many hops for each packet being sent. Recently, the author proposed a routing method, GSLP-w(GPSR-based Source-Location Privacy with crew size w), that enhances location privacy of the packet-originating node(i.e., active source) in the presence of multiple assets, yet taking a path of not too long. In this paper, we present a refined routing(i.e., next-hop selection) procedure of it and empirically study privacy strength and delivery latency with varying the crew size w(i.e., the number of packets being sent per path). It turns out that GSLP-w offers the best privacy strength when the number of packets being sent per path is randomly chosen from the range [$1,h_{s-b}/4$] and that further improvements on the privacy are achieved by increasing the random walk length TTLrw or the probability prw that goes into random walk(where, $h_{s-b}$ is the number of hops of the shortest path between packet-originating node s and sink b).