Besides CapOne and the HSBC banks (HSBC, Household, Orchard Bank, etc.) what other companies use a soft pull to pre-qualify you for a credit card?

I want to establish more credit so that I can bargain and build my score. I want to be able to get a good interest rate on a home loan in about two years, so I want to have better score. Right now my score is 610, 606, and 616, I also have a Vantage score of 685.

I have made some past mistakes and most of them will fall off my report by July of next year. I anticipate my FICO score will be in the upper 600's or low 700's after this happens. I pay the balance in full each month and only use a little to show utilization rates between 1% and 15% so that the score stays higher. I have a 2 yr 6 mo average for history.

I currently have a Merrick Account ($3/mo fee), which I love. 2 CapOne's ($39 fee), 1 Household ($0 fee - Yes!), 1 Marathon Oil card, 1 Bealls, and a FingerHut card. (I never use the FingerHut!) All of which show excellent history. I want to add one or two more so I can have more bargaining power in the future with CapOne, since they have never given me a credit line increase beyond the initial one and it has been 1 year 2 months on one card and 9 months on the other card. (One is the Classic Platinum and the other is the Cash Rewards card.) (I will hate when they take over my Household card, as I expect they will do something crazy like charge an annual fee, I hope it doesn't happen until after the bad things fall off my report, then they won't have as much of an option to do so. I don't trust them.)