Well OK so I used False Swipe and put to sleep, a level 2 Pidgey. Then I used the only Pokeball I had-A Premier Ball. So It didn't even shake once before the Pidgey got out! Are they meant for catching Pokemon?
Premier balls have the same catch rate as a poke'ball. They just 'look cooler'.
http://www.serebii.net/itemdex/premierball.shtml
