I recently (October 2011) was approved for both the Chase Sapphire Preferred and the Amex Blue Preferred. In both cases, I was given a low limit due to a mistake on my credit report, which has now been taken care of. For the Sapphire, at least, I was given the minimum limit after a reconsideration call. The Amex was approved outright, though also low limi. I use the Amex exclusively for the groceries and gas categories, so I'm never in danger of needing a huge limit; I generally put about 200-2500 per month on the Sapphire as my main spend card. The only other card I have so far is the Freedom, which has a reasonable limit as I've had it since before the mistake showed up.

All that to ask: which is better, asking for a limit increase on one or both cards, or not? I am jumping into the churning game in 2012, so I can see it working either way. If the issuer has to do a hard pull for the increase, that's bad and not worth it. If getting a couple new credit cards and thus increasing my overall credit availability is just as good, then it's a wash. And if Chase especially has an approach of "we will extend this person only X dollars of credit", then it might work in my favor to have the lower limit, and perhaps score an extra card.

So I turn to the experts...my thoughts are just hypotheses. What's the best approach in the real world?