The transversely averaged description of an axisymmetric convective column over a maintained source of weak buoyancy, given by Morton, Taylor, and Turner (1956), is extended to encompass the tall updraft over a large-area fire, with provision for large density differences in a rather arbitrarily stratified, moist ambient. The plume zone (from the completion-of-burning height to the onset-of-condensation height for water vapor), and the capping cloud (from the onset-of-condensation height to the altitude at which the updraft stagnates), are treated such that the solution may be patched to a previously described model for the flaming zone (from the pyrolyzing-fuel-bed surface to the completion-of-burning height). The relative contributions of combustion-generated and entrained-ambient water vapor to in-column moisture content are systematically investigated, along with the dilution with altitude of smoke density of the convective column. According to results from the simple model, the density discrepancy between in-column fluid and ambient fluid at the same altitude typically vanishes in the unsaturated plume, so a capping cloud is found to be a region of negative buoyancy. The desirability is noted of cloud-chamber experiments to examine the efficiency of rainoul/washout of smoke for cases in which sufficiently strong convection results in the rapid growth of condensed water droplets (and/or ice particles) to precipitating sizes. Such cases are not encompassed by the modeling, which is limited to the case of small droplets that are lofted by the updraft