The LE is going to be harder to get deals on. The more decked out stuff you add the more you can negotiate. Let's say they have a base model with nothing. You aren't going to get much off unless it's been sitting. If there's another trim with some nicer stuff (sunroof, NAV, audio, leather, ec) then you can negotiate easier. If it has been sitting longer on the lot you can work towards it.
If you get the barebones then it's really difficult because stealerships aren't making much at a lower markup; they wont be willing to negotiate as much. But if they add heated seats, radio/speaker upgrade, etc AND you tell them that you're willing to pay a bigger cash down if they add some options then there's your wiggle room.
Sometimes you have to compromise but you should always see what you can get.