Gehrtzm
Please look at your QuickTime export setting with a check mark next to Limit data rate to _______ kbps and try typing in 7000 for starters and adjusting the bitrate there to find the compromise between bitrate, quality, and quality.
If you can get the file size that you want, it is my understanding that the best Mac way to go is H.264.mov or H.264.mp4.
ATR