Brainstorming is defined in our work as the process of getting smart ideas and through the junk ones. If an idea that is infeasible the group will start criticizing the owner.
Patrick Mcdermott the author of Zen and the Art of System Analysis propose a unique way to perform Brainstorming.
Brainstorming is about filling the board with crazy ideas without limitation. The most important key is having fun. He insists that Brainstorming is about Quantity instead of Quality. As long as your teams are freely shooting their ideas without any criticism or BUTs/Howevers/NOs. You should get the best out of it.
The more your teams place ideas on the board the more you exercise their brain to produce even more ideas. The quality doesn't matter at this stage. You can later select, combine, remove ideas to create qualitative ideas.
Patrick says he measures the success of his brainstorming sessions by how loud his team laughs and the number of complains he get from the next rooms!