Simple recovery mode with mirroring - is that possible? (The usual 'I'm not a real DBA, but I need to handle this somehow' disclamer here)

We have a database with Full recovery model that doesn't really need a Full recovery model... only it does. 

Some context first: the database in question contains some data used by the nightly job scheduler (e.g. server connection parameters, queue state etc.). This data doesn't really warrant for the point-in-time recovery or even, for that matter, for backups, because it's much easier to re-create the whole database from scratch. At the same time it's a production database with mirroring enabled, so it can stay online and available if we switch to DR server for any reason. 

So we are in a Catch-22 situation: either we switch to Simple and lose the automatic failover setup (which is kind of necessary for us to have), or we keep Full and take regular log backups that we don't actually need, otherwise transaction log file will keep growing (with data that, again, we don't actually need).

The only solution I could come up with is scheduling an automatic job that discards all transaction log data, but I've been wondering if there is a saner way to handle this.
Mirroring uses the transaction log to redo everything at the mirror site.  In simple recovery model, the transaction log is effectively transitory and only enough information is kept in the log for undo/redo to keep the database consistent during crash recovery. So Database mirroring is not possible in Simple Recovery model as it is not supported.