Is there a way to turn direct message text alerts off but keep updates on?

Is there a way to turn text alerts for direct messages off completely, but still be able to tweet to your own account or @ reply from your phone. Every time I get a DM I get a text and these are both annoying and very much unwanted, however I still want to tweet from my phone.

After searching the FAQ I can only find something that tells me how to turn off updates and DM's but not keep updates on and stop DM's. I consider the DM alerts spam and want them to stop altogether. Does anyone know how to stop them without having to send a seperate OFF (insert username here) message to twitter for each person I follow. This would be both time consuming and expensive.

If there is not currently a way to do this, please please devise one, I can't be the only one who is annoyed by the text alerts surely.