The first thing your eye does is search for edges, and it fails. A face floats up out of a wash of pink and yellow, half-dissolved in what looks like fog but is actually chiffon: a sheer veil pulled taut over features that only slowly resolve into a person. The mouth is parted. The eyes are shadowed hollows. It takes a beat to realize you are looking at Mick Jagger, and another beat to feel faintly uneasy about how long it took.

That blur is the whole point. The portrait was made by David Bailey, a friend of Jagger's who had been photographing the Rolling Stones since 1964. He wanted the veil to summon Katharine Hepburn in The African Queen, that gauzy, sun-bleached glamour of old cinema. Jagger, for his part, was reluctant to be shot wrapped up like this. The tension between star and lens is baked into the image: this is a frontman famous for his mouth and his swagger, reduced here to a soft smear behind fabric, glamorous and slightly suffocated at once.

Look at how the color behaves. There is almost no hard line anywhere. The gauze catches light at the crown of the head and bleeds into amber at the edges, so the figure seems lit from within, like something seen through a fever. The features that survive the haze are the darker ones: the sockets of the eyes, the smudge of the brows, the open mouth. Everything else surrenders to the veil. In the top left corner sits the only crisp element on the whole cover, the words The Rolling Stones in a slim, restrained serif, dark against the pale wash. That typographic calm is what makes the face feel so strange; the band name is composed and legible while its singer is anything but.

The design that framed all this was by Ray Lawrence, though the sleeve credits managed to spell his name 'Ray Laurence.' Together with Bailey's photograph, the layout was deliberately quiet, letting the single dissolving head carry the entire front. In the original 12-inch pressing the portrait was printed roughly life size, so a buyer held Jagger's actual-scale face in their hands, veiled and staring back through the gauze.

What you see is remarkable partly because of what you don't. The chosen image was the survivor of far stranger ideas. Goats Head Soup, released on 31 August 1973 through Rolling Stones Records, takes its name from a Jamaican dish made from a goat's body parts, and one early cover concept was exactly that: a literal goat's head simmering in a soup pot. The label decided it was unsuitable for a sleeve, but the band liked it enough to keep it alive as a poster insert tucked inside the album.

There was a wilder proposal still. In mid-May 1973 the design company Hipgnosis, celebrated for its Pink Floyd work, was brought in and pitched the Stones as centaurs and minotaurs roaming an Arcadian landscape. Aubrey Powell remembered a shoot booked for one in the afternoon at their Floral Hall studio in Covent Garden, and Mick and Keith drifting in around five. The half-man, half-beast fantasy went nowhere. Set against those rejected concepts, Bailey's veiled head reads almost as a retreat into elegance: one face, one fabric, no mythology, just an unnerving softness.

The front is only part of the story. Open the gatefold and the same treatment continues, with Mick Taylor, Bill Wyman and Charlie Watts each wrapped in similar fabric, their faces given the same dissolving veil. Keith Richards was placed on the back cover. The whole package becomes a set of matching apparitions, five men delivered to the buyer as ghosts behind gauze rather than the leering rock outfit the public expected.

The music inside courted trouble the sleeve only hinted at. The closing track, originally titled 'Starfucker,' had its name changed to 'Star Star' at the insistence of Atlantic Records chief Ahmet Ertegun, and even then the BBC banned it on 10 September 1973 for its obscene lyrics. There is a neat irony in that: a record whose cover hides everything behind a decorous veil, carrying a song too blunt for radio.

Critics could not agree on what they had. In Rolling Stone, Bud Scoppa called it 'one of the year's richest musical experiences,' while Nick Kent in the NME heard a band running low on originality. The public settled the argument its own way. The lead single 'Angie' went to number one in the United States and the top five in Britain, and the album itself topped the charts in the UK, the US and several other markets.

So the veiled head endures as the face of all that: the compromise cover that beat a boiling goat's head and a herd of centaurs, the image of a reluctant Jagger blurred into something both beautiful and slightly wrong. Look at it long enough and the softness stops feeling like glamour and starts feeling like disappearance, a star vanishing into the very fabric meant to flatter him.