On the college track team we use to have to do plyometrics and other speed stuff when we were dead tired from running. Since I was a highjumper, explosiveness was #1. My coach would have us run two 400 meters, then two 200 meters, then 4x 100 meters at almost top speeds, then do plyometrics, like setting up low hurdles and having us jump over four in a row x two footed hops. Like boing, boing, boing, boing! stop. or jump up 3 stairs, pause, down 2 and as soon as your feet hit, back up 3.
If you lift, I'd do something similar, like hit the bag 20 times in a horse stance or (vary the stance) as fast as you can. Make contact, but don't worry bout power. Do this when you are dead tired from an arm workout, and do a few sets.
I'm speaking in generalities. Come up with something that practices speed, and focus on bing fast while you do it. Even just punching a bag think fast insead of hard. When you train, strength comes easier than speed or endurance, whenever you add new muscle, it needs to be trained to be fast and tireless.