Method of operating a long direct-fired inclined counterflow rotary kiln for the thermal treatment of material and counterflow rotary kiln adapted for same, whereby material to be treated is introduced into the kiln at the inlet end and treated material is evacuated from the kiln at the outlet end, whereby a main combustion zone extends inside the kiln over a distance of ¼ to ⅓ of the internal length Lint of the kiln, whereby a supplementary combustion zone in which supplementary combustion takes place with an oxygen-rich oxidant extends inside the kiln over a distance from the inlet end of at most ¼ of the internal length Lint, and whereby no combustion takes place in a heat exchange zone located between the main combustion zone and the supplementary combustion zone.