Former Gov. Rod Blagojevich will get a new sentencing hearing, but it may not actually reduce his time in prison.

The 7th U.S. Circuit Court of Appeals ruled Tuesday that faulty jury instructions mean Blagojevich’s conviction on five of 18 counts should be vacated.

But the court wrote that he should remain in prison while his case proceeds and cast only mild doubt on the sentence U.S. Judge James B. Zagel imposed in 2011.

“It is not possible to call 168 months unlawfully high for Blagojevich’s crimes, but the district judge should consider on remand whether it is the most appropriate sentence,” Judge Frank H. Easterbrook wrote in the 23-page opinion.

The five convictions stemmed from Blagojevich’s attempt to get a Cabinet position from then-President-elect Barack Obama by appointing his friend, Valerie Jarrett, to Obama’s vacant U.S. Senate seat.

Jurors could have found Blagojevich guilty for trying to get money or a private-sector job in exchange for that Senate seat. But Zagel also said they could convict him of extortion if the Cabinet spot was all he sought.

That’s not a crime, that’s politics, the appellate court wrote.

“The instructions treated all proposals alike. We conclude, however, that they are legally different: a proposal to trade one public act for another, a form of logrolling, is fundamentally unlike the swap of an official act for a private payment,” Easterbrook wrote.

If jurors believed Blagojevich was merely aiming for a Cabinet spot, it doesn’t violate the federal Hobbs Act — the basis for two of the convictions that makes it a crime to interfere with commerce by way of robbery or extortion.

The ex-governor didn’t rob anyone, the court wrote, and the evidence didn’t show that he made attempts at extorting a position by claiming an “official right” to a job in Obama’s administration.

A public position can be held or occupied but not “obtained,” and case law says something that can’t be “obtained” can’t be the subject of extortion, the court wrote. In addition, a public job is not property and thus cannot be subject to the legal definition of extortion, the court held.

Another law that underpinned one of Blagojevich’s convictions makes it illegal to solicit “corruptly anything of value.” But the law does not apply to legitimate wages, salary or other compensation “in the usual course of business” in political job-seeking, the court held.

And “as we’ve pointed out, the ‘usual course of business’ in politics includes logrolling,” Easterbrook wrote.

Blagojevich was also convicted of wire fraud in connection with the proposed Senate seat deal, but that charge may not hold up either, Easterbrook wrote.

“That the negotiations used the phone system is indisputable, but where’s the fraud? Blagojevich did not try to deceive Sen. Obama,” he wrote.

Easterbrook noted that a prosecutor contended Blagojevich denied the public of the right to his honest services.

But that argument “supposes an extreme version of truth in politics, in which a politician commits a felony unless the ostensible reason for an official act also is the real one,” Easterbrook wrote, using the hypothetical example of a governor who proclaims a public employee to be the “best person for the job” even if the governor doesn’t truly believe his or her own statement.

But if the U.S. attorney’s office opts for a new trial on the vacated counts, Easterbrook wrote, prosecutors can proceed without arguing that his attempt to secure a Cabinet position is a crime. Prosecutors could instead focus on the allegations that Blagojevich tried to trade the Senate seat for a lucrative private-sector job.

“Because many other convictions remain and the district judge imposed concurrent sentences, the prosecutor may think retrial unnecessary — but the judge may have considered the sought-after Cabinet appointment in determining the length of the sentence, so we remand for re-sentencing across the board,” Easterbrook wrote.

The court concluded by noting that the range for Blagojevich’s sentence was between 360 months to life imprisonment, but Zagel gave him some reductions — even where he may not have deserved them.

The panel noted that he got a sentence reduction for accepting responsibility, “even though he pleaded not guilty, denied culpability at two lengthy trials, and even now contends that the evidence is insufficient on every count and that he should have been acquitted across the board.

“That’s the antithesis of accepting responsibility,” the court wrote.

Judges Michael S. Kanne and Ilana Diamond Rovner concurred in the opinion, U.S. v. Rod Blagojevich, 11-3853.