Amazon itself has not yet provided financial details backing up its boast. It will report fourth-quarter results Jan. 29. But Web measurement service Compete Tuesday provided fresh data illustrating Amazon's dominance and insights into the online retailer's holiday success.

Compete's research showed that Amazon's share of traffic compared to the top 10 discount retailers and department stores hit 39% in December, up 18% from a year ago. Overstock.com and CircuitCity.com (since liquidated), by contrast, saw their share of visits plummet 35% and 44%, respectively.

Amazon shoppers also logged 4.5 trips to the site last month, compared to the average of 2.1 among rival retailers online.

While acknowledging Amazon's much-vaunted customer service and purchase recommendations, Compete highlighted the company's aggressive promotion of its Amazon Prime program as another factor helping to lift holiday sales. For $79 a year, Prime provides members with free two-day shipping on most orders with no minimum purchase required.

A free one-month trial offer drove up enrollments, with an average of 3.4% of Amazon customers signing up throughout the holiday season. Compete found that 53% of total online purchases made by Prime members in December were made at Amazon, compared to 29% for non-members.

Nearly half the time Prime customers shopped online, and Amazon was at least one of the retailers they visited. And 40% of the time, it was the first stop.

"It's clear that even when members don't buy a product on Amazon, membership in the program increases the likelihood they at least consider Amazon for the purchase," stated Compete analyst Matt Pace, on the firm's blog.

He suggests that other retailers may take a page from Amazon's book. "As pressure mounts on retailers, developing strategies to counter Amazon's new "ace in the hole" will be key to their ability to continue to attract, engage and retain the best online shoppers," he wrote.

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