I just put together a series of pretty successful brainstorms — good work, happy designers, lots of deep thinking that is continuing even after the pitch it was for. One of the keys to the success, at least in my mind, was that the brief was (brief and was) presented a day in advance of the actual brainstorm. The second key was that there were subsequent brainstorm sessions. Grokking new ideas takes time, re-aligning thinking requires unconscious and conscious work, and concepts take hold at deeper levels and in parts before bubbling up in an expressable form.
My piano teacher gave me a student assignment book (I could never keep track of what I was supposed to do) and the little note in the front seemed in line with my recent ‘no silver bullets’, ‘no acts of divine inspiration’ ‘creativity is a habit’ screeding:

I blogged this before, emphasizing 1) break it down; 2) master the components and add it together; 3) clean it up & go deeper; 4) make it sing.