If you don't keep a deadline, you break your promise.
A deadline, by definition, does not move. If it moves again it's a liveline.
What is the root of the problem ?
When you think that doing your work will take 5 days, you tell your boss and customer that you will finish the work in 2.5 days to please them. And it takes finally 3 days with lots of stress and a broken promise and credibility loss.
I propose to change your habits. Don't divide your estimation by two but multiply it by two.
When you think that doing your work will take 5 days, you tell your boss and customer that you will finish the work in 10 days. And it takes finally 6 days with no stress and polished work.
In the eyes of your boss or customer, you just gave them an unexpected gift.
This is what I call the unexpected deadline.
Broken promise take on your self-confidence account, delivering the unexpected save on it.