@Anonymous, it's always a soft pull with Capital One, although the soft pull is likely the one used for your last account review. Customer service reps can tell you when your last account review was and when your next one will be. The score used is most likely the classic Equifax FICO 5 (FICO 04), which is the same score used for mortgage lending.
How much have you spent on the card each of the past three or four months? And what's your current limit? Unless your score is low or unless something bad sticks out on your report, spending is the number one consideration for granting Captial One CLIs.
Don't worry too much about the amount of your request. Put in a number you're comfortable with, and don't worry about it potentially leaving money on the table. Since Capital One started asking customers to request a specific amount, I've received two CLIs. In both cases, Capital One offered more than I requested.
As mentioned, no clock is reset if you're denied. You can request again tomorrow. But I think the more practical thing would be to request again in a month or so.
