They are pretty strict about credit limits on the BA Amex and are very fond of granting you only one increase every six months. If you apply within that period and they turn it down, they will reset your clock.

The BD MBNA card is another story. They usually want to up your limit until you have enough credit to buy Belgium. I could finance an invasion of Iran on the lunatic credit limit they've nudged up on my card, without my ever asking for it.