When you say second set of jaws I assume you have what's called solid jaw model. One set (of 3 jaws) is dedicated for smaller diameter range, another set for larger diameter range. Nothing wrong with them but one downside is like you are experiencing. If they need to be replaced, you need to find a set matched to the chuck model meaning: jaw width, backside scroll threads & ground & matched to hold round stock concentrically in the 1,2,3 positions.
A better way to go IMO is 2-piece jaws. You remove the cap screws & reverse the jaws 180-deg to accomplish this. Since the jaws sit on tenons of the inner moveable jaws, they come factory ground on all surfaces so they are accurate on both diameters & vertical stair surfaces & not dependent on the scroll. You can buy replacement jaws & soft jaws or make fixture holding accessories since the tenon dimensions are a known published standard.
Bison quality precision self-centering scroll chucks.
www.bisonchucksonline.com
This is a 6.25" dia D1-4 direct bolt on style.
Bison 6 1/4" 3-jaw forged steel body chuck, 2 piece jaws, D1-4 mount
www.bisonchucksonline.com
The Set-Tru style
@Darren mentions usually is the same style of chuck in terms of the business end of chuck body & jaws, but the backplate + rear end of chuck is different to accommodate dialing in any remaining chuck runout via 4 opposed set screws, kind of like a 4J independent jaw principle. You can also see that style of chuck on the first link. Bison calls theirs Set-Tru, Gator calls it Tru-Turn, others have their own name... similar principle. Careful when you price one. The ST chuck can be about the same price but the backplate can be spendy. You require both.
I mention Bison mostly as a terminology reference. They are great chucks but spendy. But sometimes they come up for good prices. Asian chucks can vary from great value to garbage, so very hard to provide feedback without specifics. Usually returning them for quality issues is a big headache due to weight & country of origin, so choose carefully there.
A collet chuck is a completely different animal. If you are looking for one of those as opposed to 3J, or in addition to 3J, we can advise on pros & cons.
