Level 5 is 2nd party? I'm pretty sure they develop for the DS(DQIX, Prof Layton,Inazuma Eleven) which means not second party anymore.
Definiton of a Second Party: In the video game industry, a second-party developer is a developer who, while being a separate entity from any console manufacturer, is tied to a specific one usually through contract or partial ownership and makes games specifically for that console manufacturer.
Anyway my Favorites are Naughty Dog, and Insomniac.
Edit: Oops missed the part in the OP where you said it is disputed. Sorry.







