After too many iterations of providing "some wild-ass guess" estimates and them turning into hard deadlines, I now try to champion a No Estimates[0][1] approach with stakeholders.

There is often understandable resistance to this at first. To address concerns, I find it helpful to share with stakeholders that a reasonably accurate estimate, one which could be legitimately used in planning concerns, is really only possible in one of two situations:

  A) the outstanding work is a carbon-copy of a previous
     effort, such as the second time provisioning a data
     center for the same system.

  B) the remaining new functional work is determined
     by the team to be in the last quartile and is
     well-defined, including remaining risks to
     successful completion.

Micro-estimates are the enabler of micro-management. A healthy team identifies the highest priority tasks to perform and does so in descending order, where priority is defined as risk to project success.

0 - https://www.youtube.com/watch?v=MhbT7EvYN0c

1 - https://www.goodreads.com/book/show/30650836-noestimates