I would concur in my own experience with what was said above. It doesnt need to be running, but any sort of longer duration aerobic work. Flag football, jumprope, shadow boxing etc. Get your resting heart rate down to the low 50's and your recovery is going to be much better.
Shorter rounds, such as 2 min rds, you can rely MORE on your anaerobic system if need be, but you can also forsake that need if your aerobic system is better conditioned.
Listen folks, your 2-3 day a week conditioning of less than 20 minutes will not get you prepared for fighting. You need aerobic, and anaerobic.
Suck it up, do long distance one day, sprints the next. You get bored? mix it up, hill sprints, sled sprints, 2 miles, 4 miles, 10 miles, bike, jumprope etc. Then, train hard in your sport. spar, hit pads etc.