Alternator Removal 3.2?

Simple question, I am removing my alternator, to replace the voltage regulator. Does one remove the wire at the starter motor, and remove the whole unit and its aluminum bracket with that wire attached, or can the back cover of the alternator be removed and the wire disconnected at the alternator back itself, and then pull the unit out? I ask as this has proved a bit more of a pain to remove than I expected, so before I jack up the other side of the car, remove the bottom panel for access to the starter, etc. I thought I would check. I don't see any alternator replacement thread in Fchat history, I will have to solve for that while doing mine.

 

The alternator wire needs to be removed from the starter, and the unit pulls out with that wire attached. No way to get the heat cover off and access the wiring while the alternator is in situ, or even loosened as the altermator wire is not long enough to pull the unit out much without its fremoval from thew starter.