You can use custom avatar, but the function is a bit buggy. As Remote and Eagle have pointed out, there is a way to avoid this problem. Listen carefully, I'll only explain it once:
1) From your User CP, click "Edit Options".
2) Click "Change Avatar" at the bottom.
3) Click "Browse" and find the avatar on your hard drive, or enter the URL.
4) Finally, check "Use custom avatar".
5) Submit modifications.