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I'm happy with my weight, but I still need to lose fat. What's the best way?
If you still need to get leaner, you will need to get rid of fat. So if you maintain your muscle mass and lose fat, you will need to lose weight.
Very few people can put muscle mass on at the same time as losing fat, which is what you are saying if you don't want the scale weight to change. People can do that over a period of time, but when you break it down, most lose the fat and then turn around and bulk to gain the muscle back.