Eminem's representatives say they should have received more compensation over National Party's copyright breach for the song Lose Yourself.
The battle over the use of the song has reached the Supreme Court, where the lawyer for American companies Eight Mile Style and Martin Affiliated said the latest decision from the Court of Appeal should have awarded additional damages for the breach.
The companies, who co-own the copyright to the song, are seeking leave to appeal a decision to lower the costs National should have to pay over the breach.
In 2017, the High Court deemed Eminem Esque, a song used in a National Party election ad in 2014, breached copyright of Eminem's song Lose Yourself.
Justice Helen Cull instructed the party to pay $600,000 to Eminem and his representatives for using the alternative version.
The party lodged an appeal against the fee and in December last year, the Court of Appeal ruled the National Party would pay only $225,000 in damages.
Lawyer for the companies, Garry Williams, today told the Supreme Court in Wellington the Court of Appeal had erred in the way it decided on costs.
Williams said his clients should have been compensated for losing their rights not to have the song used in a certain way.
"We had a monopoly right. Essentially, by engaging in the infringement, they took from us that ability to control the use of that."
He said Eight Mile Style and Martin Affiliated would have required a premium for the use of the song.
"In these circumstances they have essentially got the work for cheap."
He questioned whether additional damages would have been awarded in a situation where the song had been used to promote a white supremacist party.
Williams also said the Court of Appeal's consideration of what alternatives the National Party could have used were irrelevant to the costs decision.
"In this case we would say something comparable is an iconic work."
According to lawyer for the National Party, Greg Arthur, the Court of Appeal said in assessing additional damages, the conduct of the defendant must be considered.
Williams had not cited any authority which ignored the defendant's conduct, Arthur said.
There was no authority he knew of where additional damages was ordered when the defendant's conduct was not at fault.
The National Party bought Eminem Esque from a company called Beatbox, which in turn bought the licence from California-based music library Labrador.
The court has reserved its decision.