WASHINGTON — The Supreme Court seemed skeptical Tuesday of a former Puerto Rico senator’s bid to avoid a second trial on bribery charges.

The justices heard the first arguments of their new term in two cases that underscored their pedestrian caseload on a court that is down one justice for at least a couple more months and possibly longer than that.

While the eight justices began their first full term without Justice Antonin Scalia, who died in February, protesters gathered outside the court to call for Senate action on the stalled nomination of Judge Merrick Garland to fill Scalia’s seat.

First up was an appeal from former Puerto Rico Sen. Hector Martinez-Maldonado and a prominent businessman. They were convicted on one charge and acquitted on another related to claims that Martinez-Maldonado traded political favors for a trip to watch a boxing match in Las Vegas. A federal appeals court threw out the conviction because the jury’s instructions were flawed.

Now the Justice Department wants to try them again. The two men say the Constitution’s protection against being tried twice for the same crime should bar the second trial.

Lisa Blatt, the Washington lawyer who represents the defendants, said the case highlights prosecutors’ propensity to add charges to improve the chance of a conviction.

“With each additional charge, a conviction rate starts out at 68 percent and it jumps to 88 percent,” Blatt said.

But Justice Ruth Bader Ginsburg said it is possible the jury was aware of what Blatt described.

“The jury might have taken care of that in this case,” Ginsburg said, by convicting the defendants on one charge and acquitting them of the other.

In Tuesday’s other argument, the justices considered whether a person is guilty of scheming to defraud a bank if he steals money from a customer’s bank account, but causes no financial harm to the bank itself.

The dispute involved a California man who illegally siphoned about $307,000 out of a Taiwanese businessman’s Bank of America bank account. Lawrence Shaw seeks to overturn his conviction, saying he’s not guilty of bank fraud because the bank suffered no monetary loss.

A federal appeals court rejected that argument and it appeared most of the justices were equally skeptical. Nearly every justice seemed to indicate that it was enough for the bank to have some interest in preserving the money in the customer’s account.

Justice Stephen Breyer injected a ripped-from-the-headlines moment into the argument when he referenced the robbers who took more than $10 million worth of jewelry from Kim Kardashian West in Paris.

Suppose someone shows up at Kardashian West’s door and says, “‘Here I am, your local jewelry cleaner.’ Gets the jewelry. Wouldn’t you think that was fraud? Even if she’s insured. Even if he thinks she’s triple insured. Even if he thinks that, in fact, this isn’t even her jewelry, that it was just loaned her on the occasion by a good friend,” said Breyer, who has a penchant for inventive hypothetical questions.

Decisions in both cases are expected by the spring.