How can I ice other mobsters in Mafia Wars as a high-level player?

I am trying to get some of the achievements that require icing other people, but having a very hard time with it.

I am winning most fights with ~25 damage on the other player, but no matter how many times I attack them it never seems to be enough. Over the last 2-3 days I've tried repeatedly attacking the same person dozens of times and they don't go down. I suspect that if I keep at it I will eventually get them, but considering how long it is taking to knock out one person, how am I ever expected to get the achievements like ice 500/1000 enemies?

I suspect the problem is that I am a relatively high level player (level 793) so it is only offering me mobsters to attack that are pretty high level also. Meaning, they probably have a ton of health. I'm sure if I attacked low level players I could probably do this a lot more quickly, but how do I find them in the game as a higher level player?

Anyone have advice to offer on whacking other mobsters once you have gotten in the 500+ level range?

Okay, it appears I was over-thinking this and by trying to be too clever I was making it harder on myself. I'm making some progress on icing people now.

Here are my tips:
1) Don't fight people with the X next to their name. I think it means they are dead and it doesn't seem to want to let you ice dead people.

2) Don't repeatedly fight the same person. It is pointless. For some reason I don't understand you never seem to be able to ice them.

3) DO randomly attack people (excluding the ones in #1 above) until you a) beat them and b) get the power attack button. Then power attack them until they are iced or you accidentally kill them. If you accidentally kill them instead of icing them move on to the next person.

4) Fighting people that are closer to your own strength/level seems to show the power-attack option more often. So don't bother trying to pick out weaklings. However, also don't pick fights with people 500 levels higher either.

It is still slow going, but I iced 3 people so far today and I hadn't been able to ice a single person in 4 days of playing prior to that. I am still a little fuzzy on the game mechanics, but this strategy seems to be working so I am going with it.

Update:
5) You don't have to win the fight to ice the other fighter. If you are fighting just for the ice count. Go ahead and power attack even if you lose as long as you are doing good damage on your attacks.