If you are a Twitter user, you can now get Twitter notifications about new tweets, replies and direct messages right on your desktop with a Google Chrome extension. Using Twitter Notifier for Chrome will allow you to get rid of desktop clients, however, you have to remember that this extension will only display those tweets and not allow you to do anything else like replying or viewing it on Twitter.
I ran a few tests to check for DM and replies notifications and they were almost instantaneous. By default the extension is set to display all the tweets along with replies and DMs, so you might want to visit chrome://extensions to change the settings for it to only display @reply and DMs if you want.
Have fun with the new desktop notifications from Twitter. Download Twitter Notifier for Chrome.