Network proof systems based on first-order specifications over channel traces are incomplete unless reasoning over the interleaving of communication events is permitted. Relatively complete trace-based proof systems using temporal logic have been described, but full temporal logic is more powerful than necessary. Using the interleaving approach, we isolate the expressiveness required of a relatively complete trace logic. A hierarchy of temporal logic subsets is then defined; a certain subset is shown to have necessary and sufficient expressive power for relative completeness.