I recently got a Cap 1 with a $300 CL. I maxed it out with a BT, and got the first statement with a $15 minimum due. I paid $25 online so they are gonna report a $275 high balance in the next 10 days. Once they report, I'll pay it down under $24.75 so the util is under 9%.
They've promised me a CLI to $500 if I pay it ontime the first 3 months. Once that happens, I'm going to max it out again by depositing a convenience check, and once they report a new higher high balance, I'll again pay it down under 9% util.