You were absolutely right. I've also been using my SLR for nearly a decade; nevertheless, I find that the shakeness seems to happen mostly while using the compact digital camera. Perhaps, it was a bit improper and unsteady posture or so in addition to the lighter weight camera ( possible to move around easily ). Stay fit is also another suggesting in addition to using the heavier camera. I don't really trust those camera equipped with the image stabilizer because it makes the camera shooter lean toward carelessness. Just a personal comment.
Use a three inch tripod. I used this little trick with my SLRs for years. Get a three inch piece of wooden dowel. You need good strong teeth for the next step. Place the dowel in your mouth and bite down firmly. Rest your Digital camera on the dowel. It will, of course be close to your face, and it will stay rock solid "shakeless".