Sarah Catt, 36, from Sherburn-in-Elmet, North Yorkshire, who was married but had been having an affair for seven years, was about 40 weeks pregnant when she took drugs she bought on the internet to induce her labour.
She claimed that the baby was stillborn and buried his body – but has not revealed its whereabouts.
Mr Justice Cooke, sentencing her at Leeds Crown Court last September, said the seriousness of the crime lay between manslaughter and murder.
He said she would have been charged with murder if the baby had been born a few days later and she had then killed him.
Catt pleaded guilty to administering a poison with intent to procure a miscarriage.
Yesterday Lady Justice Rafferty, heading a panel of three judges in the Court of Appeal, said it was an extraordinarily difficult sentencing exercise, but the term was excessive.
Lady Justice Rafferty said that Catt’s complicated obstetric history, which involved adoption, seeking termination and concealment of pregnancy, threw up a “potential for disturbance, personal misery and long-lasting difficulty”.
Catt, who was described at her trial as “cold and calculating”, had no relevant previous convictions and a psychiatric report excluded mental disorder.
She sobbed in the dock throughout the hearing in London.
Lady Justice Rafferty referred to a letter of “remarkable restraint, dignity and loyalty” from Catt’s husband, which spoke of his hope that the couple and their two young children could stay together as a family.
She said the facts of the case were “mercifully highly unusual”.
Catt had waited until the end of her pregnancy term before premeditatedly destroying her child, lied about it and had prevented a post-mortem examination with its potential to determine the cause and timing of death.
Her persistent refusal to reveal the location of the body was originally said to be a consequence of legal advice, but was now put down to her not being “emotionally able” to address the issue.
Lady Justice Rafferty added: “Mrs Catt caused the death of a foetus at term. She intended to do it. She planned what she did with some care. She ensured that when she delivered the infant, it was in private. Somewhere, there is a body.
“She had known by October 2009 that she was pregnant and she had ample time to seek a lawful termination. She was not without experience in that regard.”
As a consequence of medical reports, she said, the trial judge had no option but to treat Catt as a normal rational individual, who did what she did for reasons of her own, never adequately explained.
In Catt’s favour was her guilty plea, the appearance of remorse, the difficulty she had in forming an emotional attachment to an unborn child and the fact she was a good mother to her children, whose development was adversely affected by her absence. The judge concluded that a “wise disposition” of the case should never take its eye off two young children and a “notably forbearing husband”.