A cross-sectionally averaged model is used to study several aspects of the physics of a bubble plume rising in a stratified quiescent liquid. Scaling analyses for the peel height, at which the plume momentum vanishes, and the neutral height, at which its average density equals the ambient density, are presented. Contrary to a widespread practice in the literature, it is argued that the neutral height cannot be identified with the experimentally reported intrusion height. Recognizing this difference provides an explanation of the reason why the intrusion height is found so frequently to be much above predictions and brings the theoretical results in line with observations. The mathematical model depends on three dimensionless parameters, some of which are related to the inlet conditions at the plume source. Their influence on the peel and neutral heights is illustrated by means of physical considerations, scaling analyses, and numerical results.