Amex likes to see a lot of (responsible) card use, from what I understand. When I got my BCP, I basically put all my expenses and ran all my charges on it for the first three months and paid off the entire or nearly the entire balance before the statement cut each time. That way, I kept a low util reporting on my credit file but showed Amex a high internal card utilization. I have heard often that Amex prefers one large payment over lots of smaller payments along the way, but then again I also heard from someone who worked at Amex or something that they do not care one way or the other. I usually made two payments each month, one to pay the small remaining balance after the previous month's statement cut and one large one to pay the current balance a couple days before the end of the billing cycle. At any rate, my original CL was $7500 and I ran $5-6k total over the first three months, requested a $7500 increase, and was given $6900, which brought my Amex CL to roughly double my only other card's limit at the time. So that's what worked for me! I'll add that I waited beyond the 60 days to wait for Amex to SP my credit report again and made sure that I had optimized my overall util for when they pulled.
If you haven't seen this already, read this great guide on the Amex 3x CLI - it helped me a lot:
http://ficoforums.myfico.com/t5/Credit-Cards/The-Definitive-Amex-3X-CLI-Guide/td-p/1811071
