lower movie size for "the New iPad" (need advice)

Hi, I would like to ask about watching movies on the iPad 3. Basically I've got some BR movies that I'd like to put on my iPad 3. However, the file sizes are humongous, going up to 10 GBs.

This time I'm not so concerned about file type (.avi, .mp4 etc.), but I'm concerned about the file size. I'd like long movies to be around 2-3 GB (max) and medium-length movies to be around 1-2 GB, but good enough quality for watching on iPad 3.
Can I "compromise" between quality and low file size? As you guys know the iPad 3 has twice the linear resolution of previous iPads, and I don't want to waste the quality available.

Is there a way where I can do this? I usually use HandBrake (on Mac) but I'm not too sure of the "variables" and sometimes I convert movies from avi to mp4 and the file size becomes 3 times as big.

Please advise, and thanks for reading! :)