The paper presents LA-MAC, a low-latency asynchronous access method for efficient forwarding in wireless sensor networks. It is suitable for current and future sensor networks that increasingly provide support for multiple applications, handle heterogeneous traffic, and become organized according to some complex structure (tree, DAG, partial mesh). It takes advantage of the network structure so that a parent of some nodes becomes a coordinator that schedules transmissions in a localized region. Allowing burst transmissions improves the network capacity so that the network can handle load fluctuations. At the same time, the method reduces energy consumption by decreasing the overhead of node coordination per frame. The paper reports on the results of extensive simulations that compare LA-MAC with B-MAC and X-MAC, two representative methods based on preamble sampling. They show excellent performance of LA-MAC with respect to latency, delivery ratio, and consumed energy.