depends where you got the alternator's from!
Remember, if the person rebuilding the alternator is having a bad day, the
customer will get the end result.

could be a snuffed out voltage regulator too, which is built into the
alternator.

Try going to a different place to get one.

Turns out, there's a wire that goes under the radiator, across the
front of the car, that was dead-shorted.  Ran a new wire, and all
seems fine.

Interestingly enough, my mechanic noticed that the idiot light wasn't
coming on with position one of my ignition switch, and that the bulb
was good. This might be a symptom for anyone with this same problem to
look out for.

-Bob