A thought, here.. is it the "physical" size or the file size, they are objecting to?... if it's the file size, I can recommend something that I posted about in Photoshop.. it's called Caesium.. yes, that is the right spelling.. it's free at Source Forge.. you can google it but you'll end at the same place.

Caesium is quite good. It will reduce most images by quite a substantial amount, while keeping image quality... ran across it by accident a while back and have been using it ever since. Lou.

P.S.

While it says UP TO 90%... don't EXPECT that every time, lol.

"..... and that was when things got interestiing."