The former Pakistan captain Salman Butt and the teenage fast bowler Mohammad Amir will remain in prison for their full terms of 30 months and six months respectively, after their appeals against the sentences imposed at the spot-fixing trial were dismissed by the Court of Appeal on Wednesday.

Butt and Amir's cases were heard in front of a three-man panel headed by the Lord Chief Justice, Igor Judge. Neither man attended the hearing, which was wrapped up inside two hours as Lord Judge stated that cricket would be "utterly impoverished" if the original punishments were allowed to be overturned.

"This is a notorious and essentially simple case," said Lord Judge after hearing the submissions from the players' lawyers. "It was spot-fixing. Three no-balls were bowled, in effect, to order. It was a betting scam, and they were very well rewarded.

In the original trial, Butt had pleaded not guilty on two counts, conspiracy to cheat and conspiracy to accept corrupt payments. His counsel, Ali Bajwa, admitted for the first time that his client had been implicated in the plot to bowl deliberate no-balls during the Lord's Test in August 2010, but argued that he had only been tempted in a one-off capacity by the size of the bung, £150,000, offered by the News of the World.

Bajwa presented a skeleton argument in his client's defence, drawing parallels with the MPs expenses scandal, in that the fall from grace from a high-profile position should be taken as punishment in its own right. Butt, he added, was a "broken man" as a result of his involvement in the scandal, but 30 months was a "disproportionate" punishment.

Furthermore, Butt's defence argued that seeing as he had not actually bowled any one of the three no-balls at the centre of the plot, there was a case of "objectionable disparity" between his sentence of 30 months and the 12-month jail term received by Mohammad Asif, who has lodged a separate appeal against his conviction having brought in a new defence team.

However, in a damning summary, Lord Judge described the former Pakistan captain as a "malign influence" and reiterated the opinion of Justice Cooke, who had presided over the Southwark trial, that he was the "orchestrator" of the plot. "His duty as captain was that if there was the faintest whiff of corruption, he was to step in and stop it," Lord Judge added.

"This corruption was carefully prepared," he said. "It was not the spur of the moment or a sudden temptation to which either applicant succumbed ... These three cricketers betrayed their team, the country they had the honour to represent, the sport that gave them their distinction, and all the followers of the game around the world.

"What was required of them was that at all times they should give of their best. If for money or any extraneous reward, this cannot be guaranteed ... then all the advantages enjoyed from those who watch cricket will eventually be destroyed."

In normal circumstances, Lord Judge added, he would have ruled Butt's appeal "unarguable", but he wanted to hear his submission in conjunction with that of Amir, towards whom he showed some sympathy in describing him as a "prodigious talent lost to cricket", but whose failure to co-operate fully with the ICC hearing in Doha in January ultimately undermined his appeal.

Amir's counsel, Henry Blaxland, had called for his client to be released immediately, on the grounds that a suspended sentence would suffice in the circumstances, given the time he has already spent in jail. Blaxland argued that the age of Amir, who was just 18 at the time of the offence, should also be taken into account.

Amir's decision to plead guilty was "courageous", added Blaxland, while the public remorse he showed in his final statement to the court at Southwark was "worthy of full and proper recognition". However, the Lord Chief Justice, a cricket follower, remarked that he had spent a lot of time "trying to bamboozle the ICC" during the Doha hearing.

"The situation for Amir was much less culpable," said Lord Judge. "But we cannot give the view that it was extinguished. He was open to the malign influence of Butt, but he can have been in no doubt about the risks and dangers of corruption, and how they would be dealt with. It was an elementary part of his education as a Test cricketer."

"This prodigious talent has been lost to cricket," he added. "Cricket will be poorer for the loss. But in the longer term the game would be utterly impoverished if the court did not recognise that this is criminal conduct of a very serious kind that must allow for a criminal sanction. A short custodial sentence was appropriate. We see no reason for interfering in the decision of the court."