This will work on Firefox and should also work on Chrome with a little adjustment. You can start posting a tweet straight from the browser address bar instead of having to navigate to the Twitter website and click on the new tweet button.
In Firefox, create a new bookmark with the following properties:
Name: Tweet (or similar)
Keyword: tw (or whatever you like)
Description: Tweet something
Now, with this bookmark saved, go to the address bar and type: tw Just testing. Then press Enter. A new tweet composition page should show up with the words Just testing. Finish off the tweet as wanted and click Tweet.
Is the tweet composition page unavoidable? Maybe not, but I don’t see an easy way to tweet directly from the address bar. And maybe that’s for the best–giving you a chance to finalise things before you publish for the world to see.