The test simulates what happens when the front corner of a vehicle going 40 mph crashes into a car, tree or other object.
The 2014 Honda Pilot, Kia Sorento, Mazda CX-9 all rated poor and Consumer Reports is no longer recommending them.
"We cannot recommend a vehicle that does poorly in this crash test, especially when others have proven they can do well," Consumer Reports Auto Testing Director Jake Fisher said.
The new Insurance Institute's small overlap test is harder for many cars than its older head-on collision test. When hit head-on, cars have crumple zones in the front of the car that absorb much of the impact.
Fisher says generally cars that don't do well in a crash test, were designed before that test was instituted.
"Carmakers engineer cars to pass these tests. Even though these are 2014 models, they were designed years ago before these standards were even introduced," Fisher said.
Fisher says if you own one of the cars that rated poorly, don't panic.
"You're not driving a death trap. Your car is just as safe as when you bought it. It's the standards that continue to improve," Fisher said.
But if you're in the market for a new mid-size SUV, Consumer Reports has some recommendations. The Toyota Highlander earned top scores at the test track and did well in the Insurance Institute's new crash test.
Another good choice is the Acura MDX. This luxury SUV costs a bit more, but it also earned high scores both at the track and in the crash test.
We contacted the three manufacturers who had one of their car ratings downgraded.
Honda released this statement: "American Honda leads the industry in third party crash test ratings with more vehicles rated top Safety Pick and Top Safety Pick + by the Insurance Institute for Highway Safety than any other manufacturer utilizing the same body structure as the 2014 Pilot. The 2013 Honda Pilot was rated an IIHS Top Safety Pick and according to them, 2013 Top Safety Pick designees like the Pilot 'continue to offer a high level of protection.'"
A spokesperson for Mazda says, "The Mazda CX-9 was designed before the IIHS's new stringent, small overlap frontal crash was incorporated into their test regime. The CX-9 received IIHS's top rating of good in their frontal moderate overlap and side impact tests and also got an overall 4-star rating in NHTSA's new car assessment program tests.
ABC7 News reached out to Kia, as well, but did not hear back from them.