I love the Jazz III's to bits, but even before I used them, I hated the way picks would flop around and were stupid difficult to get positioned right. I used to heat up a paperclip with a lighter and melt "grip holes" into the plastic to get better purchase, and even then it wasn't perfect.
Then I found the Max Grip Jazz 3's and haven't looked back since. They come in 3 kinds (no ultex, but really, there's no need. The only difference I can tell is the ultex version is actually impossible to bend, where the other 3 are nearly impossible to bend)
From left to right, the Jazz III Max Grip Carbon Fiber, Jazz III Max Grip Nylon and Jazz III Max Grip Stiffo.
The Carbon Fiber is the most flexible, by which I mean "If you force it, it flexes". Realistically unless you're after playing with a house brick, its stiff enough for anyone. The Stiffo version and the Nylon version seem to be as strong as each other, so very slightly less stiff than the Ultex Jazz IIIs. I think thats something of an illusion though, since the Ultex is so hard that it feels like it "clunks" on the strings rather than just picking them.
So far I can't decide if I like any better than the others, apart from I don't like the Ultex, since the Ultex ones aren't available in Max Grip, and slip around.
The only downside I can find after months of using these as my regular picks is that you have to order them online, and the grip after a few weeks gets skin and oil in it, so you periodically end up taking a nailbrush to them to get the grip performing at its max capacity again. But even that is really minor to be honest. The grip works even when dirty, just not quite as magically well.