I once read someone give similar advice about estimation. What stuck with me most is that if someone pressures you to change an estimate, it's no longer an estimate. Most managers don't actually want estimates.
Ran it up the flagpole. It got cut in half. Fortunately I didn't need to change the schedule I had drawn up. I just said each box is now half a day. (This was before we used computers for this sort of thing.) As I recall, the job came in very close to my initial estimate.