The "Cone of Uncertainty" which Steve McConnell talks about in his book on estimates has been brilliantly helpful for me. Essentially you give a range of "best possible" and "worst possible", and as the project progresses you adjust those two numbers and at the very end of the project they converge on the actual number. That deals with the precision and accuracy issues while allowing you to be competitive. It's similar to your "confidence level". I also tend to write a lot of assumptions into estimates, things like "assuming your team gets us access to your environment by day X"...

J.Ja