Getting the Estimate right?

NoEstimates: How To Measure Project Progress Without Estimating

Can we ever get the estimate right?

Sometimes we think something needs 3 weeks but the powers be want it in 2 weeks. Estimation is said to be best done when you get it from the person who is going to do the actual grinding. But what about the person who says 2 to 3 weeks but turns out that it can be done in 2 to 3 days. Or what about the person who thinks that a change can be done in an hour but with verification and presentation and final acceptance of the change, it runs into 3 weeks.

The corect answer lies somewhere in between the under estimation and the over estimation.

Or how about estimating after getting the feet wet?