Leeya was on a life-support machine for 12 days before it was switched off
A father who "used his baby as a tool to avoid deportation" has been jailed for life for her murder, and must serve a minimum of 16 years.
Olusola Akinrele, 34, was sentenced at the Old Bailey for killing seven-week-old baby Leeya, who died in December 2006 with a catalogue of injuries.
Nigerian Akinrele, who lived in Cambridgeshire, denied murder. The court heard he had overstayed his visa.
A judge ordered his automatic deportation on completion of his term.
Leeya died in Ipswich Hospital when a life-support machine was turned off 12 days after ambulance staff found her apparently lifeless body in her Whittlesey home.
The court heard more than three weeks before, Leeya had suffered 22 broken ribs, a fractured skull and a fractured thigh.
Judge Clegg said: "When she was not asleep, Leeya must have been in excruciating pain."
Akinrele had "little or no interest in his daughter", he said.
Akinrele entered the UK on a student visa in 1997 but failed to return to Nigeria when that expired in 2001.
"You simply saw her birth as something which might help you avoid deportation," the judge told him.
He said Akinrele saw his daughter's "incessant crying" as an "irritant".
Akinrele was described in a psychiatric report as "a manipulative individual with psychopathic traits".
He was convicted of murder by a jury at Ipswich Crown Court.
The baby's mother, Kelly Inman, 22, previously pleaded guilty to allowing her death and was cleared of murder.
Judge Philip Clegg said Akinrele had "little or no interest in his daughter"
She received a total sentence of five years, having also been convicted of a separate fraud charge.
She had called 999 after Akinrele's final attack on their daughter, carried out in what the judge described as "a sudden flash of temper".
The court heard the baby had undergone checks by midwives and a health visitor in the two-and-a-half weeks after her birth and her condition had not raised concern.
The judge found the injuries she sustained later represented at least three separate attacks.
He said that Leeya must have been shaken and "come into forceful contact with something hard" at least once.
Severe force had been applied to her right leg and she had also been bitten.
On December 18 2006, Akinrele was alone upstairs with his daughter when he carried out the attack which killed her.
"The [final] attack must have taken the form of either violent shaking or throwing the child down hard."
He told Akinrele: "Your victim could not have been more vulnerable.
"It is to be expected that any child should look to its parent for protection. What you did to Leeya was a terrible breach of trust."
Gail Adams, from the UK Border Agency, said: "This was a terrible crime and we will seek to deport Akinrele following completion of his sentence."