One sticky issue: you may not know what the interest rate actually is for the chunk you paid.
e.g.
1. Charge $100 at the grocery store, 12% APR
2. Pay off $10
3. $200 Cash advance from ATM, 20% APR
4. Pay off $10
Guess what, you have several $10 chunks to pay off, but at various interest rates. Most issuers pay down the lowest APR first, regardless of any chronological ordering. So if you know the policy, you should be able to figure it out, but if you continue to charge while you are paying down your debt, there could be a lot of chunk-juggling to maintain a sane view of what you owe.