I wonder how old that article is? It says the alumiconn connectors did well in initial tests, but are too new to be considered reliable. Yet on the top of the page it shows a picture of them as good to go, versus a picture of a wire nut with a slash through it. It also says the Alumiconns are the next best method if the COPALUM system is not available.
I personally don't see a problem with the Alumicons, they have a terminal screw style mount that is like a circuit breaker, and those are rated for aluminum wiring.
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I think Larry's reply was a little bit tongue in cheek, the problem in my opinion with retightening connections is that if they were loose, arcing, and carbonization will have ruin the Integrity of the device and the wiring at it. the alloy they used back then is subject to work hardening, and I frequently find that just removing device from the box and straightening the wires will cause the wires to break off, either at the screws or where any sharp bends are.
Stuffing aluminum wiring back into the usually shallow boxes of that era is putting a lot of strain on the conductors, that's why I mainly replace them with new ones... That and they are frequently near or overfilled, and getting more pigtails of any type in there is near impossible.