Former cabinet minister Chris Huhne is challenging a court order for £77,750 in costs relating to his prosecution for passing speeding points to his former wife.
His case will be heard by judges at the Court of Appeal in London on Tuesday.
Prosecutors had claimed more than £100,000 from Huhne, who pleaded guilty last February.
Both Huhne and his ex-wife Vicky Pryce were imprisoned for eight months for perverting the course of justice.
The former Liberal Democrat climate change secretary admitted last year to asking Pryce to take his speeding points to avoid losing his licence, and Pryce was convicted of having agreed to do so.
The pair were charged over an incident in March 2003 when Huhne's BMW car was caught by a speed camera on the M11 motorway between Stansted Airport, in Essex, and London.
He was an MEP at the time and in danger of losing his licence, having already accrued nine penalty points.
The costs order was made in May by Mr Justice Sweeney at London's Southwark Crown Court, who rejected Huhne's legal team's original offer of £25,000.
Pryce, who was convicted by a jury last year, was ordered to pay £49,200.
During Pryce's trial, the prosecution alleged that she had chosen to take the points but later plotted to expose Huhne after he revealed he was having an affair with an aide and ended the couple's 26-year marriage.