Apple will give free protective cases to buyers of its latest iPhone to alleviate the so-called “death grip” problem in which holding the phone with a bare hand can muffle the wireless signal.

Apple CEO Steve Jobs announced the giveaway on Friday during a news conference at the company’s headquarters, even as the company denied that the iPhone 4 has an antenna problem that needs fixing. The more than three million people who have already bought the iPhone 4 and new buyers through September 30 will all be eligible.

People who already purchased the $29 “Bumper” cases will be refunded.

Mr. Jobs began the event by saying, “We’re not perfect,” but was quick to point out that no cell phone is perfect. He played a video showing competing smart phones, including a BlackBerry from Research in Motion, losing signal strength when held in certain ways.

Phones usually have an antenna inside the body. In designing the iPhone 4, Apple took a gamble on a new design, using parts of the phone’s outer casing as the antenna. That saved space inside the tightly packed body of the phone, but means that covering a spot on the lower left edge of the case blocks wireless signal.

Consumer Reports magazine said covering the spot with a case or even a piece of duct tape alleviates the problem. It refused to give the iPhone 4 its “recommended” stamp of approval for this reason, and it had called on Apple on Monday to compensate buyers.

On Friday, in the company’s first remarks following the magazine’s report, Mr. Jobs said Apple was “stunned and upset and embarrassed.”

Mr. Jobs said the iPhone 4’s antenna issue isn’t widespread. He said just over five out of every thousand users have complained to Apple’s warranty service, and less than 2 per cent have returned the device.

“We’re not feeling right now that we have a giant problem we need to fix,” Mr. Jobs said. “This has been blown so out of proportion that it’s incredible. I know it’s fun to have a story, but it’s less fun when you’re on the other end of it.”

Analysts have criticised Apple’s first responses to reports of reception problems as dismissive, and cautioned that the company shouldn’t come across as arrogant.

Earlier, Apple said the problem with the phone was primarily a software issue, with iPhones displaying more cell phone signal “bars” than they should have been {hbox}” leaving people who believed they had a strong signal frustrated by dropped calls. Apple issued a software update Thursday it said would make the number of bars shown on the phone’s face more accurate.

But Consumer Reports painted the problem as much broader. On Friday, the magazine said the free cases were “a good first step toward Apple identifying and finding a solution for the signal—loss problem of the iPhone 4.”

Mr. Jobs apologised to buyers who had less-than-perfect experiences with the new device.

“We’re going to do whatever it takes to make them happy and if we can’t make them happy we’re going to give them a full refund and say we’re really sorry we inconvenienced you, and we’re going to do better next time,” the CEO said.

The refund applies even for those who have long-term contracts with AT&T, the iPhone’s exclusive U.S. wireless carrier.

Jill Small, an iPhone 4 owner who runs a fashion consignment business in Los Angeles, said she was of two minds about the antenna issue. On the one hand, she hadn’t noticed any problems with the phone. On the other hand, if there really is a problem, she finds Apple’s response inadequate.

“A case you can get for $10, but the antenna issue you’ll have for the life of the phone,” she said. “If it was my business, I’d do a recall.”

Ed Brown, who sells accessories for Apple products from a table set up on the street outside an Apple store in New York, said he’s had people come hunting for cases for the iPhone 4 because they’ve heard of the antenna problem. But they’re not mad at Apple.

“They love Apple and they’re dedicated customers,” Brown said. “I haven’t heard much negative feedback.”

Jobs’ health

Mr. Jobs, a cancer survivor, also addressed a question about his health on Friday.

“I’m doing fine. I was even better earlier in the week (when) I was having a vacation in Hawaii, but I decided this was important enough to come back for,” he said. “I’m doing great.”