In order to ameliorate the overload at an overloaded network node that is discarding some of the SMSs it is receiving, when a node is overloaded with received SMSs, it sends a message to the nodes from which it is receiving SMSs of that fact and includes a parameter indicating the extent to which it is overloaded. That parameter, for instance, may be the percentage of SMSs that it is receiving that are being discarded. With this information, the sending node can determine a percentage of the pending SMSs during such conditions that will help remove the overloaded node from the overload condition more quickly. Furthermore, the network protocol may be adapted to include a priority parameter in SMSs. Then, when an SMS sending node knows that a node to which it is sending SMSs is overloaded, the sending node may decide which SMSs to send to the overloaded node based on such priority information.