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Prince William and his wife Kate have yet to announce a name for their new newborn son -- but bookmakers have tipped George and James as likely contenders for Britain's new third in line to the throne.

Choosing a name can be agonising for any new parents, but the Duke and Duchess of Cambridge are burdened with the added knowledge that their child's name is headed for the history books.

Experts say the couple are guaranteed to plunder William's illustrious family tree in picking a name for the little prince, but will settle on one that is in keeping with their image as "modern" royals.

"I do think that Prince William is quite a traditionalist -- that's my feeling," said Charles Kidd, editor of the Debrett's genealogical guide to the British aristocracy.

"I wouldn't be surprised if they use a name that is already familiar in the royal family -- something that has royal associations."

But royal-watchers may have a while to wait for the big announcement.

William's name was not revealed until a week after his birth in 1982 -- and when Charles was born in 1948, the wait lasted an entire month.

There was "no news on names" on Tuesday, a royal official said.

"The royal family quite like to do things slowly," said Kidd.

"It's quite dignified to have a bit of breathing space between the birth and the announcement of the name."

But he added: "The Duke and Duchess of Cambridge seem very organised. I would be surprised if it took them longer than a week."

The royal family tree is full of boys' names still popular among British parents today, including George, James, William and Richard -- but there are also plenty that have gone out of fashion, such as Ethelred or Athelstan.

Bookmakers have been doing a roaring trade in bets on the baby's name.

The majority of punters will now be cursing after putting money on a girl's name -- Irish bookmakers Paddy Power said around 60 percent of gamblers had guessed the baby would be female.

But there is still time to win back their losses if they pick the lucky boy's name.

George is now the Paddy Power favourite at 6/4 followed by James (11/4), Alexander (7/2) and Louis (8/1).

But James, the name of Kate's brother, is the "red-hot" favourite with Ladbrokes, although the odds on Henry -- the formal name of William's brother Prince Harry -- have been slashed from 50/1 to 5/1.

At the other end of the spectrum, Wayne is trading at 250/1 -- although a bet was earlier placed on Kai, the name of footballer Wayne Rooney's son, at 1000/1.

There have been six British king Georges, including the current queen's father George VI, whose story was brought to life in the Oscar-winning 2010 film "The King's Speech".

Royal experts say the name emphasises the continuity of the monarchy, while it also seems modern -- it was the 9th most popular choice for baby boys born in 2011, according to the Office for National Statistics.

James is more problematic. There have been two British kings with the name, the second of whom was deposed in 1688 after he sparked a constitutional crisis with his pro-Catholic policies.

Other names also have unlucky royal connotations -- there was the so-called "bad" king John who ruled from 1199 to 1216, while William's father Charles, heir to the throne, bears the name of Charles I, who was beheaded in 1649.

The royal naming game is made more complicated by the fact that by tradition, British princes have a string of middle names.

Edward VIII was among the unluckiest in this regard -- his full name was Edward Albert Christian George Andrew Patrick David, the last four after the patron saints of England, Scotland, Ireland and Wales.

His family called him simply David.

William has three middle names: Philip after his grandfather, Queen Elizabeth II's husband Prince Philip; Arthur, like the legendary 5th century British king; and Louis after Philip's uncle Louis Mountbatten, who was Charles's mentor.

When William was born, it was rumoured that his mother Princess Diana wanted to call him Sebastian or Oliver, while his father preferred Albert.

Ultimately, if Baby Cambridge is not keen on his name, he can always change it later -- all monarchs are free to choose a new name once they rise to the throne. The queen's father was called prince Albert before reigning as George VI.