The Supreme Court has rejected one of Kim Dotcom's attempts to get a hearing from it - and ordered him to pay $2500 in costs to the United States.

However the written judgment issued by Justices William Young and Ellen France today is separate from another case brought by Dotcom and three others which will go before the Supreme Court in June.

Today's ruling withholds permission to make an appeal to the Supreme Court. This relates to a judicial review begun by Dotcom to challenge aspects of the process over extradition proceedings.

The United States wants Dotcom extradited there to face criminal copyright and related charges.

Following a US application, the High Court struck out seven of the eight causes of action named by Dotcom in the judicial review.

Young and France note that the eighth cause related to a decision of the Deputy Solicitor-General to direct that clones be made of the electronic devices seized from Dotcom's homes and that the clones be sent to the US. The other three defendants in the extradition proceedings are also seeking judicial review of the Deputy Solicitor-General's decision.

The Court of Appeal dismissed Dotcom's appeal against the High Court decision, finding that the seven causes of action were either not reasonably arguable or were abuses of process.

"We are not persuaded that the proposed appeal raises matters of general and public importance," Young and France wrote.

"The applicant [Dotcom] also argues that a miscarriage of justice will occur if leave is not granted. We are not persuaded that this is correct either."