President Trump’s umbrage at the portrait of himself hanging at the Colorado Capitol may be a choice, but it is hardly novel in the annals of leaders disappointed in their representations. The 47th president turned art critic reckoned that the painter, Sarah Boardman, had “purposefully distorted” his image, which hung alongside other presidents at Denver. The Republicans will seek a new work that captures Mr. Trump’s “contemporary likeness.”

Denver’s Democrats have greeted all this aesthetic angst with a shrug, sniffing in a statement that “If the GOP wants to spend time and money on which portrait of Trump hangs in the Capitol, then that’s up to them.” Mr. Trump, though, is right when he reflects on Truth Social that “nobody likes a bad picture or painting of themselves” and that this one is “truly the worst.” He even ventures that the artist “must have lost her talent as she got older.”

Mr. Trump’s disappointment in his representation was preceded by no less titanic a figure than Winston Churchill. As depicted in “The Crown,” the artist Graham Sutherland’s edition of the British Bulldog, commissioned for Churchill’s 80th birthday in 1954, was so repugnant to its subject that it ended up in the flames. The TV series has Lady Spencer-Churchill consign it to the fire — historians finger the great man’s private secretary.

Churchill’s initial reactions to the portrait make Mr. Trump’s sound measured. The leader of England is reported to have exclaimed in private that Sutherland’s rendering made him “look like a down-and-out drunk who has been picked out of the gutter in the Strand.” The vernissage at Westminster Hall was recorded by the BBC, and Churchill took a more diplomatic tack, calling the portrait “forceful” and “a remarkable example of modern art.”

He did not intend it as a compliment, though the Lincoln Memorial reportedly served as inspiration for Sutherland. On February 27, 1860, before the 16th president was sworn, he delivered an address at Cooper Union, which concluded with “let us, to the end, dare to do our duty as we understand it.” Earlier, he had hustled over to Matthew Brady’s studio on Broadway and 10th and sat for a photograph that is now at the Met’s collection.

Some portraits of power, though, have proved deadly. Henry VIII’s courtier, Thomas Cromwell, asked the painter Hans Holbein the Younger to paint a picture of a potential fourth wife, Anne of Cleaves, for the Defender of the Faith. Cromwell pushed the match, but it proved disastrous when Henry grumbled that he had been misled and that “She is nothing so fair as she hath been reported.” Anne and Holbein survived the fiasco. Cromwell did not.

We’ve noted Mr. Trump’s eye for the link between politics and portraiture before, when he traded a portrait of President Jefferson to Speaker Johnson in exchange for one of President Polk, who expanded America’s borders and now claims coveted real estate at the Oval Office. Mr. Trump sees in the 11th president something of himself. Also, possibly, in Churchill, a bust of whom the president has restored. Sutherland’s painting was unavailable.