Additionally, distilling the water before filtering through (activated) charcoal is an excellent purification strategy. Distillation removes everything except for a few volatile organic compounds (VOCs) that evaporate at a lower temperature than the water. Carbon (charcoal) filtration removes all of these VOCs very effectively.

Using the fire to do the distillation, then using the charcoal from the fire to do the carbon filtration not only seems like a very effective purification means, but it seems almost self sufficient as long as you can find wood for a fire.