The duke discusses his last duchess as a warning to his next potential wife. He hated that she was "too soon made glad, / Too easily impressed." She was equally pleased by everything, large or small, costly or not: the sunset, for example, pleased her as much as the duke's "favour at her breast." He wanted her to value him above anything else. The worst, however, is that
[...] she ranked
[His] gift of a nine-hundred-years-old name
with any common thing, such as fruit from the orchard or a pretty white mule on which she could ride. It's true that he could have chosen to speak with her about this apparent fault of hers, but that would have required him to explain why she should love and appreciate him and his gifts more than anyone else's. His pride would simply not allow him to explain this to her. He says that if he tried to teach her,
E'en then would be some stooping; and I choose
Never to stoop.
He wants his wife to be like a pretty picture, something he can possess neatly, someone without opinions that contradict his own. The duke warns his next wife, through the Count's emissary, about how she is to behave or else he will give more "commands" that result in "all smiles stopp[ing] together."