The online credit limit generator is pretty generous. I started at I think $8000 a year ago. Some posts at fatwallet seem to indicate going over $25K might trigger a financial review, so I stopped at $24K which is plenty for me anyway.
I recently got the Starwood amex, but they only gave me $2K due to all of my other credit card shenanigans. They won't let you request a CLI for six months, but online I reallocated $10K from my blue over to the Starwood instantly. I immediately went and requested a $8K increase on the blue and it was granted, back up to $22K.