LONDON — Oliver Cromwell was given to the odd bout of brutality during his career, but no one could accuse him of vanity. Typical was his injunction to Sir Peter Lely, the German-born painter. “Mr. Lely,” the Lord Protector said, “I desire you would use all your skill to paint your picture truly like me, and not flatter me at all; but remark all these roughness, pimples, warts, and everything as you see me. Otherwise, I will never pay a farthing for it.”

Portraiture has always been a delicate business, capable of inspiring great delight or deep offense in the subject. Few sitters have skins as thick as Cromwell — or so thin as that of the late millionaire Bernard Breslauer. This week, it was disclosed that the antiquarian bookseller, who died in 2004, secretly destroyed a painting by Lucian Freud because it showed him with a double chin. The news dismayed Mr. Freud, whose 1995 depiction of a snoozing benefits supervisor sold recently for $33.6 million, making him the world’s most expensive living artist. He had hoped to include the Breslauer portrait, painted half a century ago, in an exhibition next month.

Mr. Freud commanded nowhere near the reputation he currently enjoys when Breslauer decided his effort might provide the ingredients for a roaring fire. But as an act of vandalism, it takes some beating.

Jonathan Yeo, who has captured Tony Blair, William Hague, and other politicians in oils, finds that portrait painting is a balancing act. “You try not to be too flattering or unflattering,” he said. “Some people do come with ideas in their heads: Could I lose them a bit of weight in the painting, for example. I tell them to come back when they’ve been on a diet. About one in four people who talk to me about a portrait are looking to be ‘improved on.’ I’m doing well enough now to refuse them.”

Mr. Blair, he said, was an interesting subject, appealing and likeable but able to switch mood and expression; not totally genuine.

“Destroying a work like that of Lucian Freud is a sacrilegious act,” Mr. Yeo said. “But in the end, the painting is the owner’s.”

The powerful and famous, equipped with keen self-images, tend to make the trickiest subjects. Graham Sutherland discovered this in 1954, when he took on the living myth of Sir Winston Churchill. The great man was in his dotage then, half senile, but still in power. Yet his ego was in rude health. Sutherland’s uncompromising modernist depiction of the old warhorse at bay, the result of a commission from both Houses of Parliament celebrating Churchill’s 80th year, appalled the subject. The prime minister said it made him look as though he was sitting on the lavatory, and refused to let it be hung in the Palace of Westminster. After the fuss died down, his wife Clementine chopped the painting up and stuffed it into the boiler in their basement.

Political skins remain thin. Last month, it emerged that Michael Martin, the Speaker of the House of Commons, had asked for his nose to be made smaller in an official portrait.

“He said it was too big,” the painter Andrew Festing said.

He had never had that kind of trouble when painting the queen. But then, Her Majesty has learned to take the efforts of her painters on the chin — even Mr. Freud’s work of 2001, which endowed her with what appeared to be five-o’clock shadow.

It might be thought that as digital photography leads to the promiscuous production of personal images, such concerns are confined to the elite. In fact, said Sandy Nairne, director of the National Portrait Gallery in London, portraiture is enjoying an unparalleled boom.

“It remains astonishingly popular,” he said. “There has been a tremendous revival in the last 20 years. There is more commissioning going on than at any other time. People are fascinated by the process — producing something that is about much, much more than just a likeness. It is a most demanding area of painting: The landscape never argues back; a still-life doesn’t talk to you.”

Breslauer’s decision to do away with his work by Freud was, Mr. Nairne said, a tragedy. “Even if a great painting is in private ownership, it is part of our common culture. His reaction was very extreme. There is a huge gulf between not liking a work and deciding to destroy it. In the end, it is a subjective view and none of us really know what we look like. We see ourselves in the mirror, the other way round. Only other people know what we look like.”

Is it ever right to flatter the subject — to iron out a few wrinkles or lose a Cromwellian wart?

“It depends on the nature of the commission,” Mr. Nairne said. “Joshua Reynolds is regarded as tidying people up, but there were other paintings that were very literal. Some portraits, particularly royal ones, were meant to convey a sense of power rather than hard reality.”

Portraitist Chuck Goodwin doesn’t look at you in conversation; he studies you: depth of forehead, kink in nose, the lines, the crags, the sagginess of earlobe. You can see him doing it, eyes scanning your features for yet another flaw, the hook for the portrait he will never paint. It is the artistic equivalent of being sized up by an undertaker, a hard-to-break professional habit.

His most illustrious subject to date is Lord Snowdon, whom he has known since the early 1960s. Mr. Goodwin doesn’t pretend a deep friendship, but Lord Snowdon, now 78, liked him sufficiently to agree to a portrait.

The result is a relaxed man sitting in a chair and staring into the past, his face emphasized by the barest sketching of his upper half. A pretend camera made from two cans of Schweppes tonic water sits in his lap, an amusing little prop.

Professionally, Mr. Goodwin is a late starter. After a career in graphics and interior design, he took up full-time portrait painting at the age of 60, five years ago. He puts himself in the second division in terms of marketability.

“Only Lucian Freud and a few others, such as Hockney, can paint a picture uncommissioned and then sell it by virtue of their name. I’m not in a position to paint a portrait of someone and sell it in its own right as a Chuck Goodwin. Freud could go out into the street, choose a street sweeper, paint him, and sell it for a million pounds.”

Mr. Goodwin believes there is an occasional need for diplomacy.

“If somebody wants me to paint their wife, they don’t want me to make her look like she’s had a late night. You compromise, you make the woman look younger. But even then she might say, ‘I don’t look like that, do I?’

“We don’t see ourselves as we are. Think how surprised you can be to catch your reflection in a shop window. Lucian Freud is quite cruel — they said his portrait of the queen was quite cruel — but he’s incredibly good at bringing out aspects of character.”

Mr. Goodwin sees beauty of a kind in everyone he paints.

“There is always beauty, yes. Even the ugliest face can be beautiful. It’s in the eye of the beholder.”

If only Mr. Breslauer had seen the beauty of those Freudian chins.