Wireless sensor networks are increasingly used for remote monitoring, fire detection, emergency response. Such networks are equipped with small devices powered by batteries and designed to be operated for years. They are often based on the ZigBee standard which defines low power and low data rate protocols. As network size and data rates increase, congestion arises as a problem in these networks, especially when an emergency situation generates alarm messages in a specific area in the network. Indeed, congestion occurs as the alarms converge to a specific destination, which results into packet losses and higher delays. In this paper, we propose a solution for congested links, called the PiRAT (Pivot Routing for Alarm Transmission) protocol. It is based on multi-path routing in order to add some diversity in routing the alarms. PiRAT uses intermediate nodes as pivots to reach the destination. Simulation results show that PiRAT has better performance than previous protocols in terms of packet loss, end-to-end delay, congestion and node overload.