Hi,
If you are on o2 (UK), you can register to bluebook, on the o2 website, which is a service provided by o2, once you have registered, you can set the option to save every text message sent/received. It will automatically do it, and you can manually forward on messages too, should you need to, I think they allow a gig of storage.
Maybe using that you could delete the conversations and always have access to your messages online if need be. For users outside the UK, I don't know if your service provider supports a feature the same.
I hope this helps.