This excellent poem is open to a number of different interpretations, but I personally believe that the Duke, who is the speaker of the poem, is very aware of what he is saying and how he is saying it and who his audience is. If we look at his description of what happened with his first wife, we see what emerges is a picture of a very proud man who believes that it is beneath his dignity to discuss with others what his will is. He believes his will should be anticipated:
...and if she let
Herself be lessoned so, nor plainly set
Her wits to yours, forsooth, and made excuse,
--E'en then would be some stooping; and I choose
Never to stoop.
The Duke's assertion that he will "never... stoop" presents us and the envoy with a very clear picture of the kind of character that the Duke is, and the mysterious fate of the last duchess, and the way that her "smiles stopped together" acts as a hidden threat to the envoy about the kind of wife that the Duke wants and the kind of husband that he will be. The ending of the poem could be argued to reinforce this, as by turning the attention to a bronze sculpture of Neptune, he is making it clear that his wife was just another possession, and any future wife will only be another possession as well.