Improved techniques for responding to a server that is overwhelmed with messages are disclosed herein. Messages may initially be placed in an “incoming” queue. Once accepted by the server for processing, a corresponding message may be placed in an accepted queue, and an indication is generated that the message will be processed. When the number of messages in the accepted queue meets or exceeds a defined threshold, new messages addressed to the incoming queue are rejected. Also, computing resources are allocated to the incoming queue until the messages in the incoming queue have been processed (or meet another condition). Once the incoming queue is empty or meets another condition, resources are allocated to the accepted queue. Once the number of messages in the accepted queue meets or falls below a second threshold, new messages are allowed again into the incoming queue.