In the last decade, it has proved surprisingly hard to put politicians accused of corruption behind bars. Appeals courts have reversed several convictions. And juries have occasionally thought the officeholders’ behavior didn’t meet the high standard for corruption.

Senator Bob Menendez of New Jersey, who was arraigned yesterday in a federal bribery case, is both an example of the conundrum and a test of whether federal prosecutors now know how to overcome it. In the senator’s last corruption trial, in 2017, jurors couldn’t make sense of the gifts and favors he’d received from a wealthy eye doctor. Were they illegal — or just the sort of thing friends do for each other?

Menendez, a Democrat, faces new charges for taking cash, gold bars and a Mercedes-Benz convertible. In exchange, prosecutors say, he attempted to disrupt criminal cases and used his position on the Senate Foreign Relations Committee inappropriately. He introduced a businessman who sought funding to a member of Qatar’s royal family, and he helped push through aid and weapons sales for Egypt, the charges say.

This time, prosecutors are hoping to make the indictment stick. In today’s newsletter, I’ll explain why the bar for conviction is so high — and what government lawyers need to do to succeed, including against Menendez, where previous cases have failed.

The Supreme Court is the main reason for the Justice Department’s difficulties. In a 2016 decision, the justices threw out a graft conviction against Bob McDonnell, a former Virginia governor. McDonnell, a Republican, used his office to help a businessman who’d lent him $135,000 and gifted luxury items and vacations.

But the justices didn’t think that was proof of corruption. They said it wasn’t enough for public servants to provide political courtesies, like setting up a meeting for a friend. The politicians needed to have a specific quid pro quo involving an official act or a governmental decision. The ruling effectively narrowed the legal definition of corruption.