Managers don't actually want estimates. A genuine "estimate" would be a probability distribution over a range of dates, with some point identified as the most likely delivery date and a roughly even chance of being early or late relative to that point. What they actually want is "the earliest date you cannot currently prove to be infeasible", which essentially is the near end of that date range, so there's a roughly 100% chance you'll come in after it. I've had exactly one manager who (after I explained this) admitted that was actually what he wanted, but I couldn't convince him of the utility of asking for genuine estimates.