The duke keeps the painting of the duchess behind a curtain as a means of postmortem control. That is, he wants control over who gets to see her image. As the reader comes to realize, the duke did not feel he had this full control over his wife when she was still alive, but now that she is dead and all that remains of her is a portrait, he can control it by withholding it from view.

Throughout the poem, the duke is shown to be a possessive man who regards his wife as an object more than as a person. He rues the duchess's habit of smiling for other people, particularly other men, because he is easily made jealous. He views her heart "too soon made glad" as a sign of flirtatiousness, perhaps even potential infidelity. While the poem never makes it explicit, it is implied the duke had the duchess killed as punishment for smiling too often at other men and for not valuing him above all else.

Now that the duchess is only a painting behind a curtain, her death also allows him to have complete ownership over her and control over which men get to see her smile. Since in life he prized her beauty and submission more than any other quality, she actually serves his needs better as a painting than she did as a living person.