While digging on the Internet this morning, I found a nice little plugin for WordPress, Tracked Tweets. With it, you can send a tweet of your post at the publish moment.
You can customize the tweet format, and allow auto-tweet or not.
You can too add Google Analytics stats only for the tweets.
Tracked Tweets adds a box on the bottom of the new post form. You can check the box to allow tweeting. The plug-in can user different url smaller systems, like TinyURL, bit.ly, tr.im (discontinued).
The plug-in page
Plug-in’s author website

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