Trending: Coolest Cooler shuts down after 5-year saga, leaving 20,000 backers without Kickstarter reward this morning followed through on a promised perk for Kindle users who subscribe to the New York Times on the digital reading device. Starting today, they will also be granted full access to content behind the firewall on the traditional web as a bonus.

It’s a logical move that might not sell more Kindles but could boost the motivation for existing Kindle users to pony up the $20 monthly Kindle subscription for the newspaper.

Standalone digital subscriptions to the New York Times run from $15/month to $35/month, depending on whether they include access to the newspaper’s smartphone and tablet apps. We double-checked with Amazon this morning, and a company representative says the Kindle subscription only provides access to, the website.

More info in this news release. Existing subscribers to the New York Times on Kindle can go here to hook up their subscriptions.

Update: Barnes & Noble announced the same deal for users of its Nook e-reader.

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