DETROIT — Car buyers looking to shrink their gasoline bill by downsizing will find that a number of small vehicles pack a painful punch at the pump.

Some fuel-efficient new cars or crossovers could prove costlier than expected because they were engineered to run on premium gasoline.

For example, Smart recommends that its Fortwo, the smallest new car sold in the United States, use premium gas, as do a number of more mainstream vehicles — including a number of crossovers and midsize family sedans. That may come as a surprise to potential customers attracted to saving money with the tiny car that gets a combined 36 mpg.

As of May 29, premium cost nearly 40 cents a gallon more than regular gasoline. That can add $4 to $6 to every fill-up and hundreds of dollars to an annual fuel bill.

The Fortwo — a tiny 70-horsepower two-seater developed to navigate crowded European streets — is just one of a growing crop of new small vehicles that recommend or require the use of premium gas.

Drivers traditionally have thought of premium gas as an extravagance demanded by luxury and high-performance cars, but the expensive fuel has worked itself into a number of mainstream vehicles as automakers build more highly stressed engines.

Conversely, performance-minded drivers can find some sporty cars that use regular gasoline and still run with high-test, premium-only divas.

A car or truck whose instructions say “premium recommended’’ can run on regular fuel without risking damage, but the vehicle’s power and fuel economy will not match the figures automakers advertise and owners expect.

Vehicles for which premium is required should not be fueled with regular gasoline. Most modern engines have safeguards to prevent damage from using the wrong fuel, but it is possible.

In addition to the Fortwo, other premium-burning subcompacts include the Mini Cooper, Mini Cooper Clubman and high-powered models such as the 260-horsepower Chevrolet HHR SS.

Midsize sedans that recommend or require premium include the Nissan Altima V6, Nissan Maxima and Volkswagen Passat.

Several small crossovers call for premium, including the Acura RDX, Mazda CX-7 and Nissan Murano. Among conventional SUVs, the Toyota FJ Cruiser requires premium.