In this paper we present new energy-efficient techniques to lower the packet-level error rates of application-layer connections in wireless ad-hoc networks. In our scheme, each application-layer connection is implemented at the physical level by an overlay network. Data packets submitted at the connection source are checksummed and replicated, flowing breadth-first across the overlay network towards the destination. The destination delivers the first error-free copy of each packet, in order, to the application layer, dropping packets that are corrupt or duplicate. Specifically in this paper, we consider overlays consisting of multiple parallel node-disjoint multi-hop paths. We compare this overlay scheme with the traditional scheme in which the source transmits to the destination along a single minimum-hop path. We show that even when the two schemes are constrained by identical power consumption bounds, an overlay scheme that uses multiple multi-hop paths provides significantly lower packet-level error rates in many common situations. We describe the relationship between packet error rate, the number of paths, and the lengths of each path, and show that the qualitative nature of the relationship changes significantly, depending on available power budget.