The Supreme Court has declined Eight Mile leave to appeal and Eminem's company has been ordered to pay $4500 in costs.

American companies Eight Mile Style and Martin Affiliated, who co-own the copyright to Eminem song Lose Yourself, first succeeded in establishing a breach of copyright after the National Party was found to use a soundtrack infringing the musical work of the song.

The National Party was ordered to pay damages of $600,000 to the applicants (collectively, Eight Mile) but the party appealed to the Court of Appeal on the cost of the damages, which was reduced to just $225,000.

Following the decision, Eight Mile sought leave to appeal in the Supreme Court against the Court of Appeal's decision.

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However, the country's highest court won't hear the case after declining to give leave this afternoon.

Eight Mile argued the approach taken by the Courts for its claim over additional damages was too restrictive.

But the Supreme Court was not satisfied the present case was an "appropriate vehicle" for the consideration of the issue raised by the applicants.

It said there was not a sufficient prospect of success in an argument where additional damages should be awarded in this case to justify a grant of leave for further appeal.

The Supreme Court awarded costs of $4500, plus usual disbursements to the respondents collectively and dismissed Eight Mile the leave to appeal.

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.

Questioned about the stoush in 2014, National's campaign manager Steven Joyce said the National Party thought using the music was "pretty legal".

The National Party bought Eminem Esque from a company called Beatbox, which in turn bought the licence from California-based music library Labrador.