This would sound selfless and mature coming from a 30-year-old, but Dell'Orefice was 13 at the time. She was forced to grow up quickly, under a cloud of disapproval and casual violence ('My mother was, shall we say, very hands-on,' she says, drily). The mother, a Hungarian, was ambitious for her daughter to achieve success, first with ballet (cut short by illness), then later as a swimmer (scuppered by a foot broken while skiing with a boyfriend). An ex-dancer herself, Carmen's mother was not pleased with the way her daughter was shaping up, and never lost an opportunity to demonstrate her displeasure. 'I was a sad child,' she recalls.
'I just wanted her to love me.' But life was hard. 'We were so poor that my mother would often leave me in a foster home until she could raise enough money to rent rooms for us.' Modelling helped them out of poverty. When little more than a girl, Carmen was earning $60 a week (equivalent to about £600 now), putting herself through private school, paying for her own orthodontic braces and secretly subsidising her adored father, an Italian violinist, who left home when she was small. She had gone looking for him when she was 15. 'We were close from then on, much to my mother's angst and chagrin. She did all the work, and he got all the love.'
With extraordinary candidness she details her teenage years, which seem to have featured all sorts of unsuitable men and unsavoury situations. She met, or in her words 'bought', her first husband - 'a lout' - at 16. 'I bought racehorses for him, and after a few abortions I married him at 21. I had my daughter, Laura, and by the time I was 24 the marriage was over.' There were two further failed marriages and, as a young girl under the spell of some of the greatest names in photography, many flights of romantic fancy. 'To this day I have a crush on Irving Penn,' she says, and what she describes as 'a lifelong love of Parkinson'. At the moment she isn't seeing a particular man, but makes no bones about her continuing need for physical closeness. Is sex important still? She bats straight back, 'Is breathing important?'
These days she lives in a New York flat stuffed with posters and pictures by Avedon and the rest, 'in the closets and under the bed'. Which are her favourite photographs? 'That's like asking someone to pick out their favourite child,' she answers. These were all 'fathers' to her, she says wistfully, remembering the support and comfort they provided when her own family life seemed so chaotic.
While she may have enjoyed close friendships with the men she worked with, the same can't be said of her relationship with her daughter, now in her early fifties and working as a therapist in California. Things were never going to be easy for a girl who had a goddess for a mother. As Laura has put it, 'My mother always said, "You have your good looks in your own right," but I never believed her. Because why didn't I have those long legs? And how come my hips and bosom weren't in proportion the way hers were? She was like a Barbie doll to me, and I was just not there.'
'She was coloured by everyone's attitude towards me,' says Dell'Orefice. 'And yet I always said to her, "Your mother's just your mother."' Over the years there have been periods of estrangement, and what sounds like horribly fraught, sporadic contact.
All of which would be enough to etch the face of even the most resilient mother. Dell'Orefice has her share of wrinkles, but she is an intelligent, thoughtful woman who has somehow made peace with her tumultuous past, absolved herself of any feelings of guilt and retained a calm equanimity that shows in her face. Her clear-eyed radiance must surely be underpinned by a long, arduous skincare regime, involving many different unguents and potions. How else would she look so good?
In fact, her big beauty secret boils down to nothing more complex than a unpromising-sounding product called Bag Balm, an ointment developed by a dairy farmer for softening cow teats. Now it's mainly used for equine purposes, 'and if it's good enough for horses, it's good enough for me.' She says it's like Elizabeth Arden's cultish Eight Hour Cream, but a fraction of the price. 'Three dollars ninety-nine for a year's supply!' she exclaims, jubilant. Here is a woman who likes a bargain. When I admire her expensive-looking ring, she takes great pleasure in yelling, 'Twenty-eight dollars! Banana Republic!'
As a fashion-loving but impoverished young model in the postwar years, keeping up with trends was impossible if you weren't blessed with the thrift gene. She used to buy charity-shop blankets to make coats. 'Me and Suzy Parker [the model and actress] always took our sewing-machines to Paris so we could make something to wear in the evening.' Among her friends, she has a reputation as a keen needlewoman, but even she can't hope to do justice to the five sewing-machines she now owns. 'Friends keep leaving them to me when they die.'
In recent years both a long-term partner and her mother have passed away, along with many close friends. But she's not one for mourning and regret. 'I've been busy trying to help people die a good death. I don't believe in funerals. I believe in celebrating life, and showing people, while they're alive, how much I care about them. And I don't believe in this business of burial. I'm an organ donor. Whether its my skin or my eyeballs, use whatever bits are intact and put the rest in the garbage.'
I have been looking at her intently for going on two hours now, and feel qualified to say that, at 76, Carmen Dell'Orefice is still luminously beautiful. If she were to drop dead tomorrow, and her body were up for grabs, take it from me, there really isn't a lot you'd want to bin.