The problem is already acute. Since 2000, spending by the highway fund has generally outpaced revenues; since 2008, the fund has required an infusion of $41 billion from the federal government’s general fund. By 2015, the highway fund is expected to spend more than $53 billion while collecting less than $39 billion, leaving a shortfall that Congress will be forced to make up.

As Kim P. Cawley of the Congressional Budget Office argued this summer in testimony before a House subcommittee, “The current trajectory of the highway trust fund is unsustainable.”

One choice, of course, would be to raise the gas tax. But this would surely raise the ire of many people and might be politically untenable. Some people have proposed a vehicle miles traveled tax, which could use fancy technologies like onboard GPS or mobile apps to track where we go and levy a fee in real time based on the distance, similar to electronic toll collection systems like E-ZPass. But these contraptions raise concerns about civil liberties and privacy protections (as the black box could report your whereabouts to authorities), and the extra technology might be costly to install. A blunt V.M.T. tax also misses the fact that a light car does a lot less damage to the roads than a heavy truck.

A better option is a “ton mile” fee based on how far vehicles travel and how heavy they are, so that all drivers pay their fair share to fix the resulting road damage. A one-ton car (which is typical for a compact car) that is driven 7,500 miles annually inflicts much less road damage than a two-ton truck that is driven 15,000 miles. While the gas tax captures some of that difference, as the truck driver would buy more fuel, it is not perfectly aligned.

Assessing a half-cent fee per ton mile would cost a typical American car owner about $50 per year and would cover the highway fund’s revenue shortfall, according to my calculations. And, rather than using tracking devices, the fee could be assessed during an annual sticker renewal or inspection that is conducted at state level: All the inspector has to do is read the odometer, look up the gross vehicle weight of the car’s make and model, then assess the fee. With a fee on the order of two cents per ton mile, gas and diesel taxes could be eliminated entirely.