By this point in the trip, land borders had become practically pedestrian. So the knowledge that almost everyone who crossed overland into Myanmar from Thailand did so at Mae Sot / Myawaddy meant that we were far more intrigued by the less accessible alternative route further south.
I scoured online for information on the Phu Nam Ron / Htee Khee crossing and found two helpful accounts of bloggers who had trodden the path in previous years.
Step one: take the train from Bangkok.
