I only bump pitch 2-3 notes (I'm around an A below middle C on the piano).
It's about resonance, basically. You need to change the sound of the tone, not necessarily the pitch. Once you get used to the placement of your voice, it will not strain your throat, but it does take some time to learn how to use your muscles correctly and to build them up a bit... the voice can get strained in the early days of practicing.
There are various tutorials around the 'net, and of course Andrea James covers it in her training course on DVD. It took me about 5-6 months of experimenting to find out how to change my resonance, and it made all the difference.