Is it general looseness or just drifting? Xbox 360 controllers seem to have a problem with drifting, and from what I can tell, most commonly to the left, for some reason. I have a controller with this problem as well, and after googling a lot, I found that there weren't many solutions, unfortunately. One thing that you can try is to slightly tilt your joystick in the opposite direction it tends to drift before you turn your controller and console on. It'll reset its neutral position then and can help counteract the driftiness. If it gets worse though and that doesn't help, getting a replacement is probably the best option, if you don't want to open it up.
If you do want to open it up, seeing as you've said you've bought new controllers, what you would probably need is a Torx T8 security screwdriver. I believe the older 360 controllers used a regular T8, but all the newer ones require the security/tamper-resistant screwdriver, which has a small hole in the tip because the screws have a tiny "tooth" on them. You can purchase these at any hardware store, and I've heard Radio Shack sells them (if you live in the US). I picked up one of these because I needed to open my controller and clean the buttons after they got a little squishy from playing lots of Bayonetta (hands got sweaty, sweat dried and left residue, ick).