Asking here for completeness, Mitel DECT headset connected to a 5340 works fine (up to a point) can have conversations etc. Just that you can't answer or clear down a call using the hookswitch on the headset (it doesn't answer if you pick it out of the cradle either (if its in). You can answer and use it by pressing the prime line and the cancel key.
Tested for internal calls only at present.
Anybody have any idea?