Safely deleting a child of a prefab

This is with Unity 4.1.3f3

I have a prefab with multiple child objects. One of those objects needs to be deleted. Selecting the child object, right-clicking, and selecting “Delete” does nothing.

I can “re-create” the prefab without this child object by pulling it into the scene, deleting the child object in the scene hierarchy, deleting the prefab in the project view, then re-creating the prefab by pulling it from the scene.

However, this breaks all Inspector links referencing this game object, so it’s not OK.

How can I safely delete a child object of a prefab, with “safe” defined as “not breaking inspector links”?

Put the prefab in a scene, delete the child object, select the prefab instance in the hierarchy and click “Apply”.

Note that indeed, even after you “break the prefab instance”, the “Select” “Revert” “Apply” buttons DO STILL APPEAR. Strange but true.