I wanted to down the Greench on my own, since I simply couldn't be bothered tracking anyone down to go with. Besides, I had complete faith in Ursa and knew he could do it. The one time I'd previously faced the Greench this year, my tanking buddy wanted to know how hard he hit, so I took a couple of shots to the face: about 25k a pop. Knowing the mechanics of the fight, I just knew Ursa could heal up in between. And since credit is shared if you've tagged the beast at all, I didn't forsee the horde being a problem.
Amazingly, everything went as planned. We whittled him down under half hp, almost 2/3s, before anyone showed up. There was an alliance druid, then a horde shaman and paladin. The druid kept messing with the shaman, even though all he was doing was hitting the Greench. I couldn't do anything to stop him, since I was tanking....and besides, all I could do was yell at him to stop, anyway. In the end, it looked like everyone got credit, so that was good. Ursa and I only had one close call at all, and I just taunted off him and deterrenced while he healed. Since we did the lion's share of the work and hadn't had any trouble before anyone else showed up to speed things along, I'm still calling it a strong soloing victory. :)