If renters have a reservation and are concerned about being stuck with a larger-than-wanted vehicle they should "call over there and say, 'I want the small car, and if you don't have the small car I'm taking my business elsewhere,'" Brown said.
Daniel Lemin, who travels frequently for his work as a professional photographer, recently reserved a compact car from Dollar Rent A Car in Los Angeles. He said representatives tried to "upgrade" his rental car to a minivan when he arrived.
The employees "were pretty aggressive about it because they were out of cars," he said. But "I didn't want to be faced with a $60 or more gas bill."
Lemin said he has seen the daily rental prices of SUVs and minivans decrease over the past four to five months to the point where the cars are less expensive to rent than any other vehicle available.
An Internet search by ABC News this week found Budget Rent A Car offering a daily rental of an "intermediate SUV" from Newark airport in New Jersey for $66. An economy vehicle was $76, and a compact car cost $77.
Some rental car companies do allow customers to reserve fuel-efficient or hybrid cars but those options are limited and often cost substantially more.
"There are times I've tried to rent a hybrid, and they're so ridiculously expensive at any of the rental places. I think that sort of indicates the level of demand," Lemin said.
Last week, business traveler Kumar Lakhavani booked a compact car for his stay in Washington, D.C., but when he arrived, the company was out of compacts. He was offered a larger car and refused to take it.
"I said, 'No, I'm just one person,'" Lakhavani said.
The change in rental car service is particularly stressful for frequent business travelers, some of whom must fund fuel costs themselves, he said.
"If you do a lot of driving, that ends up costing a lot of money, and apparently car rental companies don't care anymore," Lakhavani said. "About two years ago, if I had asked for an upgrade to a small SUV, it would have cost me $5 to $6 a day extra."
To increase the likelihood of getting the rental car you want — whether it's a compact or an SUV — Brian Ek, the general manager of Priceline.com's PriceBreakers travel service, suggested booking reservations as far in advance as possible.
To improve a rental car's fuel mileage, Ek said drivers should avoid sudden starts and stops, check the car's tire pressure "first thing," leave windows up and turn on the air conditioning.
"The easier you can be on your pedal the better your mileage can be," he said. "You'd be surprised — every little bit helps."
Lakhavani said rental car companies need to change their marketing strategies to fulfill a new kind of consumer demand.
"Our auto industry was for a long time in denial," he said. "They need to anticipate what's coming. If Avis came up tomorrow and said, 'Our vehicles are fuel-efficient vehicles,' they'd see a surge in people wanting to rent from Avis."