Add "delete" links to multivalue field values

I initially posted this suggestion here as a potential solution to another problem, but I think it bears consideration as an issue in itself: It's confusing and unintuitive to ask users to delete the content of a field value to signify that they want to remove the whole position at that delta. I don't think the action corresponds to the function. Much more logical, in my mind, would be to delete the contents of the INPUT at a position when what you want is a position with an empty value, and create a separate UI element for the (really distinct) function of deleting the whole position from the list—for example, a delete link or button next to each position, as depicted below. Not only would this eliminate ambiguity, it would make the act of deleting a field value both more "findable" and more "intuitive". (What is the new user left to think when there is a button specifically to "Add another item" but no corresponding button to remove one? It would not be unreasonable to assume, at first glance, that you can add but not remove.)