I use the tick twister. You can get it on Amazon for $6-$12. According to the ticktwister website the "pro" version has a hole to put in on a cord if you need to..
Remove Ticks Easily with Tick Twister®
I used it on Maggie. She had a tick who had recently bitten into her, but had not yet started to swell up, I guess he was a fresh one who was hopefully going to be killed by her K9 Advantix...He was a Lone Star tick, had a white spot that was very obvious.
It was the easiest tick I ever removed. I didn't need anybody to hold her down and I got all the tick parts out. The hardest part was just to twist, NOT pull. You are not to pull on the tick, just twist. The website has a nice video.
With tweezers you might just squish stuff that you shouldn't and probably leave the mouth parts stuck in there.