The passenger in the seat next to mine yawns contentedly as we taxi along the runway.
He hardly stirs when the engines start to roar and the plane accelerates before lifting into the sky.
By the time our sleek, six-seater jet reaches cruising height his head has dropped and his eyes have closed.
Ready for takeoff: Finally there is a way forto treat their pooches to a dignified mode of flying
During the two hour hop to Palma, on the island of Mallorca, where his family has a holiday home, my neighbour eschews his complimentary glass of Moet and Chandon champagne and is tempted neither by the inflight entertainment or the pile of glossy magazines.
He looks every inch the high flyer – prosperous, self-assured, and remarkably well-groomed. My fellow passenger, Dylan, is a dog.
He belongs to a new breed of pampered mutts who, rather than being confined to cages in the hold along with the cargo, sit in their own leather-upholstered in the cabin next to their owners.
The service is being offered by Victor - a private jet charter company. It isn’t a cheap option.
Dylan, an eight-year-old miniature Schnauzer, is being charged £1,250 for a seat on a Victor flight to Palma, exactly the same as it costs humans using the service.
Dogs have long travelled alongside their owners - but only if they are fortunate enough to be owned by someone with their own jet - but is is all about to change
The service is offered by a private jet company and it allows owners to travel alongside their beloved dogs
And a seat is what he gets, not a space on the floor at the back of the plane near the lavatories, not a dedicated mat next to the exit.
At one point, Dylan stares out of the window of the Lear40 jet and seems genuinely enthralled by the wispy cloud formation gathering a few hundred feet below.
He enjoys the landing, too, as we soar over the Mediterranean and as buildings come into focus as the pilot makes his descent.
Happy flyer: Eight-year-old miniature Schnauzer Dylan enjoyed the flight to Palma, Mallorca
Family member: It's not a proper holiday without the dog, says Dylan's owner Isabelle Frank
'How can you have a proper family holiday if you don’t take the family dog with you?' asks Dylan’s owner, Isabelle Frank, who live in Putney, south-west London.
'In the past we have put him in the hold but the trauma was terrible for both of us. It used to break my heart seeing him in a crate on the runway waiting to be hoisted on board.'
Apparently Dylan didn’t care for it much either. Mrs Frank says he began to panic as soon as he saw empty suitcases being brought out of the cupboard.
'We tried putting the cage in the house for a few weeks before travelling in the hope that he would get used to it, but he never did.
Strapped in safely: Dylan pictured before takeoff and during the flight wearing a seatbelt
Happy dog: Dylan definitely preferred flying in his own seat to taking the cargo route in a cage
'In fact, he would run in the opposite direction and was clearly in distress just at the thought of it. Look at him now. He’s his normal happy self.'
He certainly looks chirpy. Before disembarking, he pauses momentarily at the top of the plane’s steps and I half expect him to pull on a pair of flashy sunglasses or doff a Panama hat to the flight attendant.
Dog days are over: Despite the high cost the company believes many owners will jump at the chance to bring their pets on board
Of course, some dogs have long traveled in this kind of luxury. The American socialite Paris Hilton, heiress to the hotel empire, has always taken her various chihuahuas and Yorkshire terriers on trips aboard her private plane.
In this respect she took after the Hollywood actress Zsa Zsa Gabor who was at one time married to the heiresses’ great-grandfather Conrad Hilton.
Upgraded: This little terrier seems very pleased to avoid travelling in cargo
In 1989, Gabor made headlines across the world when, during a stopover in Atlanta on a flight from Los Angeles to Florida, she let her two Shih Tzu dogs out of their designated kennels and allowed them to run free in the cabin.
When she refused to lock them up again, Gabor and the Shih Tzus were briskly escorted from the plane by Atlanta police.
For dog owners as devoted as Paris, but without the resources to maintain a private jet, Victor is the company to make it possible to travel with your pet on a ‘per seat’ basis just as you would if booking for a human.
'A happy dog makes a happy owner,' says Clive Jackson, the founder of Victor, which officially launches its dog service this week.
'I realised there were a lot of people who weren’t going on holiday to places like Mallorca because they couldn’t take their dogs with them. We’re opening a door for them.
'I got talking to one woman who had seen her dog yelping in its cage upside down on a conveyor belt after she went the cargo route. She said she would never put her dog through that again.'
Mallorca has proved a good hunting ground for entrepreneur Jackson. The Spanish island is a favourite with British second home owners. Indeed, Jackson has a house there himself. He doesn’t own a dog but he knows plenty of people who do.
Lynne Franks, the PR guru and inspiration for Edina Monsoon’s chatacter in the sitcom Absolutely Fabulous, has booked a seat next month for her and Noodle, a Labrador cross.
'She is the love of my life and the thought of her being confined to a small space for hours on end and treated like cargo is appalling,' says Franks. 'Now there is a civilised way for her to travel with me. I can’t wait.'
Rule changes mean that from this year, all dogs and cats can come and go from the UK without spending time in quarantine providing they have a passport, are correctly micro-chipped and been vaccinated against rabies.
Private flights: No commercial airline allows dogs or cats to travel in the cabin with their owners and many charge high fees for cargo travel
But no commercial airline allows dogs or cats to travel in the cabin with their owners. Monarch charges around £1,000 for a cage in the hold on its London to Palma service, but neither easyJet or Ryanair carry dogs or cats even as cargo.
So, how do other passengers react to finding themselves sharing an arm rest with a dog? For my part, the company of Dylan was infinitely preferable to that of a toddler repeating every ten minutes: 'Are we nearly there yet?'
On arrival in Palma, I ask Dylan if he will remain in his seat for a photograph and he’s only too pleased to oblige.
Never again will he be put in kennels when the family goes abroad. Never again will he be regarded as excess luggage or locked in a cage 30,000ft in the air.
'Once he gets a taste for this he’ll probably want to pilot the plane himself,' says Mrs Frank.
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