A method and apparatus for processing call signaling messages during burst overloading and sustained overloading of a communications switch include processing that begins by receiving a plurality of call signaling messages, which may be call set-up messages, connect messages, call proceeding messages, call release messages, release complete messages, and/or link layer information. The processing then continues by comparing a queue occupancy level of a call processing queue with a first queue occupancy threshold. If the queue occupancy level compares unfavorably with the first queue occupancy threshold (e.g., the queue is storing more messages than desired), call signaling messages are enqueued into the call processing queue based on the types of the call signaling messages. For example, dispensable call signaling messages are enqueued in a LIFO manner while indispensable and essential messages are enqueued in a FIFO manner. Dispensable messages are those, that if dropped, have minimal impact on the efficiency of the communication switch and/or do not evoke a time-out process to release whatever communication resources have been allocated to a particular communication set-up request.