The paid version of the SMS Backup & Restore app.
In addition to all the features of the free app, this has:
- No ads
- Support for WebDAV as a backup location
- Support for compression and encryption of backups
NOTE: There is currently no support for update notifications for the app downloaded from here. You’ll have to manually download the APK again whenever there is a new version released. You can log back to your purchase history to download the APK.