Unusual Backfiring Problems

ok guys here what i got I am so stumped right now haha.

I changed the ignition box and distributor cap and it still backfires. but only at very specfic time and speed. For example I will accelerate no problem no backing firing then ill let off the gas completely and when I am about 40 to 60 when i get back on the gas just a tiny bit barley pushing the pedal it will back fire pretty bad but as soon as i give it gas then its fine no hesitation or anything. We have re built the carb but maybe we missed something? or could the carb not be tuned right even though it backfired before we rebuilt it in the same way it does now.