And one other point in favor of 2-piece jaws - every 3-jaw (and all of the relatively rare self centering 4-jaw) chucks comes new with two sets of jaws (called by various names but Inside and Outside are common choices). Unfortunately, if you buy a used 3-jaw, at least judging from the photos and descriptions on eBay, 90% of them the PO has lost the 2nd set. That isn't usually the case with 2-piece jaws. And if the removable jaws are missing, 98% of the time you can buy brand new ones from any decent machine tool supply house. Which you cannot do with one piece jaws.