I keep hearing that several teams are considering signing Kwame Brown.
That's fine, if you're just looking for a big body. But that's all he's going to offer you.
There are several other quality big men to be had for cheaper than Nene, Tyson Chandler and the like.
In other words, these are big men that you would NOT consider as starting power forwards or centers; big men that you would NOT consider to be stars or missing pieces.
Take a long look at these other big men before you consider offering Kwame Brown part or most (I can't imagine anyone offering ALL) of your mid-level exception.