I thought that there was a Havas bus that did the same route (or am I imagining things - again ?)
No, you're right. The Havaş service is timed to meet the domestic arrivals from THY etc - it them goes round to international (for those that had to clear customs) before heading to Fethiye. I dont use it much these days as it only goes as far as the otogar, previously (when it was the THY service bus) it went to Karagözler and dropped me 100m from the apartment.
Be fun and games if both are parked up outside domestic arrivals at the same time!
JF