“In return for writing the review, we will refund your order so you will have received the product for free,” it said.

Anne Marie Logan, a Georgia pharmacist, was suspicious. “I was like, ‘Is this for real?’ ” she said. “But they credited my account. You think it’s unethical?”

While the letter did not specifically demand a five-star review, it broadly hinted. “We strive to earn 100 percent perfect ‘FIVE-STAR’ scores from you!” it said.

The merchant, which seems to have no Web site and uses a mailbox drop in suburban Los Angeles as a return address, did not respond to further requests for comment. As of last week, the company (as opposed to its products) had received 4,945 reviews on Amazon for a nearly perfect 4.9 rating out of five.

Amazon is expected to sell 20 million Kindle Fire tablets this year, making the market for cases potentially enormous. But it is also bitterly competitive, with dozens of models in Amazon’s Kindle showroom. With a modest investment, VIP pushed its product far above the competition, none of which had so much enthusiasm with so little dissent. Customers like Ms. Logan, who got something they had genuinely wanted for only a small shipping charge, were of course thrilled. And Amazon racked up more revenue.

Even a few grouches could not spoil the party. “This is an egregious violation of the ratings and review system used by Amazon,” a customer named Robert S. Pollock wrote in a review he titled “scam.”