Move over, trillion-dollar coin, there is a new debt limit workaround in town — and this one sounds more sophisticated, which some of its proponents have suggested could make it more likely to work.

For years, debt limit skeptics have argued that the United States can get around the cap on how much it can borrow by minting a large-denomination coin, depositing it in the government’s account at the Federal Reserve. Officials could then use the resulting money to pay the country’s bills. The maneuver would exploit a quirk in U.S. law, which gives the Treasury secretary wide discretion when it comes to minting platinum coins.

But there have always been challenges with the idea: Treasury has expressed little appetite. It is unclear whether the Fed would take the coin. It just sounds unconventional to the point of absurdity. And now, some are arguing for a fancier alternative: premium bonds.

The government typically funds itself by issuing debt in the form of financial securities called bonds and bills. They are worth a set amount after a fixed period of time — for example, $1,000 in 10 years — and they pay “coupons” twice a year in between. Typically, those coupon rates are set near market interest rates.

But in the premium bond idea, the government would renew old, expiring bonds at higher coupon rates. Doing so would not technically add to the nation’s debt — if the government previously had a 10-year bond worth $1,000 outstanding, it would still have a 10-year bond worth $1,000 outstanding. But investors would pay more to hold a bond that pays $7 a year than one that pays $3.50, so promising a higher interest rate would allow Treasury to raise more money.

Would those higher interest rates, which would cost the government more money, pose a problem? Not technically. The debt limit applies to the face value of outstanding federal government debt ($1,000 in our example), not future promises to pay interest.

And the idea could also come in a slightly different flavor. The government could issue bonds that pay regular coupons, but which never pay back principal, or perpetual bonds. People would buy them for the long-term cash stream, and they would not add to the principal of debt outstanding.

The premium bond idea has gained support from some big names. The economic commentator Matthew Yglesias brought it up in January, the Bloomberg columnist Matt Levine has written about it, and The New York Times columnist and Nobel-winning economist Paul Krugman made a case for it this week.

But even some proponents of premium bonds acknowledge that it could face legal challenges or damage the United States’ reputation in the eyes of investors. And while it might come in different packaging, it has a lot of similarities with the coin idea. Either plan would exploit a loophole to add to government coffers without actually lifting the debt limit.

The reality that both are seen as gimmicky could keep them from becoming reality.

Of all the options the government could use to unilaterally get around the debt ceiling, “they are the least likely in our opinion,” said Chris Krueger, a policy analyst at TD Cowen.

But a workaround that hinges on the 14th Amendment could garner broader support, Mr. Krueger said. That would leverage a clause in the Constitution that says that the validity of public debt should not be questioned.

Some legal scholars contend that language overrides the statutory borrowing limit, which currently caps federal debt at $31.4 trillion. The idea is that the government’s responsibility to pay what it owes would trump the debt limit rules — so the debt limit could be ignored.

It would not be a perfect solution: The move would draw an immediate court challenge and could sow uncertainty in the bond market, even its proponents acknowledge. Still, some White House officials have looked into the option.