For those willing to go through a complicated F/R Financial Review, with a clean credit report, new credit report, even baddies that are years old, you can offer to provide any and all financial statements by request to get this CLI. Chances are that will open the doors. They will probably ask you to fax or mail copies.
However should this not work over the phone, you can also send GW copies of financial statements such as savings, W2s, and tax returns through the mail with a GW letter requesting a "Credit line increase".
There is no set time frame of 3 months, 6 months, 1 year ect. As long as you are willing to go the distance and provide hard copies to put the lenders at ease you can get much further. I am confident that this method will provide more open doors when you ask for CLIs. This can be done at any time.
This method does involve sending data about your self. You will have to decide if you are comfortable sharing this information. Perhaps a certified letter with tracking to insure it doesn't get lost in the mail.
A F/R can work for anyone to your advantage. You don't need a big paycheck. You just need to show you make enough to cover the CLI should you venture off on a shopping spree.
Who would benefit from this F/R? Anyone who can not get a CLI and can show income more than twice greater than your total available credit. After that it gets in to a grey area and odds go down.