Strip out all the junk in the MRE's you don't need or want. The accessory pack is the first thing I get rid of. I've got a lighter, don't need the matches. They suck anyways. The gum is garbage. The beef jerky is compressed dog vomit.
Take the side dishes out of the cardboard. If you're actually going to use your MRE heater, keep only the entree cardboard. If not, junk that too. The toilet paper is only good for starting fires. I'm sure you get the idea.
Then put everything you're keeping back in the MRE bag, squeeze the air out, roll it up and tape it shut.