Looking back at my past projects I often encounter this one:
A client or a manager presents a task to me and asks for an estimate. I give an estimate say 24 hours. They also ask a business analyst and from what I've heard their experience is mostly non-technical. They give an estimate say 16 hours. In the end, they would consider the value given by the analyst even though aside from providing an estimate on my side, I've explained to them the feasibility of the task on the technical side. They treat the analysts estimate as a "fact of life" even though it is only an estimate and the true value is in the actual task itself. Worse, I see a pattern that they tend to be biased in choosing the lower value (say I presented a lower value estimate than the analyst, they quickly consider it) compared to the feasibility of the task. If you have read Peopleware, they are the types of people who given a set of work hours will do anything and everything in their power to shorten in even though that is not really possible.
Do you have specific negotiation skills and tactics that you used before to avoid this?