This is a low-cost but laborious method that produces excellent results. All you need is water, at least two buckets calibrated in litres so that the sediment volume can be recorded, and a mesh for trapping the charred remains. Geological sieves are ideal but I have occasionally used medical gauze or an open-weave cloth.
In this 1989 video clip (I was shooting video tape back then) A.C. D’Andrea is processing sediment from Mochiyazawa, an Epi-Jomon (Zoku-Jomon) site in Yoichi, Hokkaido. The sample is rinsed as many times as required until no charred material is present in the water. The wet sediment is washed through a screen and the resulting material is the heavy fraction.