You can DEFINITELY drop from 21 to 13%. I went from 27% to 13%. I took the long, slow approach and don't feel like I lost any muscle. My strength even went up, although I wasn't truly "strength" training before I started dieting so had plenty of room to get stronger. I was training, but not for strength.
Suggestions? Start carefully counting calories. Keep a food journal. It's a pain but otherwise you're just guessing, and most people underestimate their intake. Track your food intake for a few weeks. During this stage, you're not dieting. You're just trying to see where you're at. Is the scale moving or holding steady? If it's holding steady, then knock about 200-500 calories off your daily intake. Stick w/ that and see if the weight starts coming off. It should. When that stops, drop another 200 or so. Repeat. Once a week, same time of day, step on the scale and/or measure your waistline. That's a decent way to track your progress.
Long story short: manipulate calories in vs. calories out. If you're burning more calories than you're consuming, you will lose weight. You can manipulate calories by what you stuff in your face and by the type/amount of exercise you do.
To lose "fat" rather than "weight," find a decent strength-training program. It should probably be lower in volume and higher in intensity. 5x5 works great but there are others. Basically, load the body enough to let it know that it needs to keep its muscle.
That's it in a nutshell. FWIW, I dropped about 2% each month I think, which was about 2 pounds/wk. on average.