Two parents imprisoned for forcing their teenage daughter to take freezing baths, hitting her and forcibly cutting her hair have had their appeals against sentence dismissed.

The woman came to New Zealand in 2007 as a refugee from the Democratic Republic of Congo and the man, the girl's stepfather, is from the Republic of the Congo.

When the couple were sentenced last year for a slew of charges relating to the abuse which began in 2010 and continued until June 2014, the court heard how the man would hit his stepdaughter until she got into a very cold bath and forced her to stay in it for long periods while her mother stood by.

The girl stopped counting how many occasions it happened after 30 such baths.

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The couple committed the abuse because they thought the girl was possessed.

The man also forcibly cut the girl's hair and told the woman to braid what was left to hide the bald patches. He also hit her and verbally assaulted her.

The man was sentenced to 2 years and three months in prison and the woman was sentenced to one year and nine months, but the couple appealed to the High Court.

In a decision released today, the judge dismissed the man's appeal against conviction and sentence, and the woman's appeal against sentence.

The man tried to appeal his conviction on a legal technicality - his charge related to offending that happened before an amendment to the Crimes Act, but the trial was carried out on the basis of the amended Crimes Act wording.

While the Crown accepted there was an error or irregularity in the way the charge was brought, the High Court ruled it did not affect a fair trial.

The man's lawyer also challenged the laying of a charge as a representative charge, saying it should have been laid as separate charges for the various incidents of cold baths, hair cutting, and other incidents where the man burned the girl's clothes and cut up her mattress.

While the High Court agreed with his criticism of the way the charge was laid, the judge was satisfied the jury would not have been confused or distracted by it.

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The woman also appealed her sentence, arguing the judge erred in declining to give a discount for the difficulties she would face in prison, due to her limited English.

However, the High Court said the woman could be regarded as "fortunate" to have had an effective 12.5 per cent discount on her sentence solely for a lack of previous convictions.

"We do not consider any further reduction is warranted," the judge said.

She also argued a home detention sentence should have been considered, but the sentencing judge noted such a sentence would be inappropriate.

"There was a need to bring home to both Mr Z and to Ms M that they were responsible for what took place and to hold them accountable," the High Court judgment said.

"Ms M was not assisted by her steadfast failure to accept any responsibility."

Her appeal was also dismissed.