The Honda Civic 2- and 4-door models both received ratings of good, which is the top rating of four, including acceptable, marginal and poor.
The new tests, adopted by the institute in 2012, are meant to simulate a common crash in the real world, one in which one front corner of a vehicle collides with a solid object, such as a tree, a wall or a utility pole.
The institute said it ran 12 models at 40 mph at walls with only 25 percent of the front bumper on the driver's side hitting the wall.
Each car tested was spun around by the tests, challenging the placement and timing of side air bags as the crash test dummy's head moved around the car's interior.
The institute said, by example, the Volkswagen Beetle's steering wheel moved five inches to the right upon impact and the side airbag did not deploy. That left only the steering column airbag, and since the dummy was thrown to the left and the steering column moved to the right, the dummy's head barely touched the airbag that deployed, hitting the dashboard instead.
"All of these issues add up to a poor restraints and kinematics score for the Beetle," the institute said.
The institute said that only four vehicles include side curtain airbags that were effective in the small overlap tests, including the two Hondas, the Hyundai Elantra and the Scion tC .
Overall, the institute said the Dodge Dart, Ford Focus, Hyundai Elantra and 2014 model Scion tC earned acceptable ratings.
The Kia Soul and Forte, and the Nissan Sentra were given ratings of poor, the lowest of four ratings.