I never queued more than 15 minutes even without TSA pre check. There is no separate queue for first class passengers
TSA pre-check is expeditious as is SWA. Check-in online if you can to trim precious minutes. Ninety minutes prior to scheduled departure is a safe rule of thumb at BHM.
Relatively quicker than you think. If you have to check in at counter and are flying around 6AM (1st flight of the day) then you Should come relatively early (approx, 70mins before the departure).
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