Many drivers aren’t looking for free upgrades when they rent cars for summer road trips. They are more concerned with fuel efficiency.

The cost of gasoline has retreated slightly from the record highs reached earlier in June, but filling up the tank can still make a significant dent in a driver’s wallet. High gas prices have created a potential double whammy for travelers given that rental rates are also still elevated.

The average rental-car price for Fourth of July weekend is $100 a day, according to data from travel search company Kayak, up from an average of $65 a day during the same weekend in 2019. While car-rental companies are expanding their fleets of electric vehicles, securing such a car can be a challenge—and typically comes at an additional cost.

Still, more people are on the lookout for fuel-efficient vehicles when renting, according to drivers, rental-car companies and others. Searches for compact cars are up 14% compared with last year, according to Kayak data, the largest increase for any vehicle class. Additionally, Kayak says, the number of searches using the site’s filter for eco-friendly cars, including hybrids and EVs, has more than doubled.

Kevin Brewer, a 31-year-old information-technology worker from Plant City, Fla., has Emerald Club Executive status with National Car Rental, which guarantees him free upgrades whenever he reserves a car at the midsize rate.

“If there’s an SUV available I will usually try to get that, because I just find it more comfortable,” he says.

On a recent trip to Colorado, however, he opted for a sedan to save money on gas. He estimates he drove between 500 and 600 miles during his getaway, spending about $80 on gas.

“I was actually pretty shocked by how cheap that was,” he says.

As the rush for more efficient rental cars picks up, supply constraints could spoil some consumers’ plans.

Rental-car companies still face challenges in securing new vehicles to expand their fleets, says Neil Abrams, president of rental-car industry consulting firm Abrams Consulting Group. The supply-chain issues make it more challenging for the companies to respond to shifts in customer demand.

“With fleets not at levels that would be ideal, travelers should expect that there will be not only issues finding a car, but in getting the precise car that you reserved,” Mr. Abrams says.

Jennifer Lewis and her family wanted to rent a hybrid for a road trip from Orlando, Fla., to Piscataway, N.J., earlier this month. Mrs. Lewis and her husband own a Honda Civic and a Hyundai Santa Fe, but they like renting hybrids for vacations to save on gas.

Mrs. Lewis wasn’t able to reserve a hybrid in advance. When the family arrived at the Enterprise Rent-A-Car location where they had made their reservation, there were no hybrids in the lot. Mrs. Lewis began researching alternatives.

“I was sitting there thinking, ‘We’re about to spend $400 on gas,’” the 42-year-old mother of two says. “I was trying to avoid that as much as possible.”

After calling other nearby Enterprise locations for nearly an hour, an employee managed to find a Hyundai Ioniq Hybrid for the family. On their drive from Florida to New Jersey, they spent only $90 on gas, Mrs. Lewis says, and renting a hybrid didn’t cost them extra.