Custom classes added via TinyMCE not sticking to images

I'm using TinyMCE on my site - version 3.5.10 (was having issues with 4). Part of the reason I choose TinyMCE is because it's so easy to add custom classes to the 'styles' dropdown in the editor (one of the 'buttons and plugins' you can turn on in TinyMCE), which then correspond to styles in your css. E.g. I always add classes for 'floatleft' and 'floatright' in order to attach these to images via the editor to add float and margin. Never been a problem with Media 7.x-1.4.
I tried using version 7.x-2.0-alpha3 so I could utilise the cool built-in views browser. But there seems to be a bug where these classes don't stick. I click on an image I've just uploaded to the editor area, choose say 'floatleft' from the styles dropdown. I then see the class get added to the p tag wrapping around the image (via the little bit of html it shows you at the bottom of the editor area), but when I click off the image, or disable rich text the class gets removed.

Has anyone else had this problem?
Can anyone offer a solution in helpfully straightforward language?

I've currently reverted back to version 1 of Media but it would be amazing to get help on this.

Thanks a lot.