The roles of rapid flow tube divergence and heat and momentum addition in one-fluid models of the solar wind and stellar winds and the role of heat addition in two-fluid models of the solar wind ae explored. It is found that under certain circumstances heat addition, momentum addition, or the rapid divergence of a flow tube can produce more than one critical point in the solution topologies of the solar and stellar wind equations. For the solar wind, additional critical points associated with rapid flow tube divergence (e.g., in coronal holes) and/or with momentum addition can lead to high expansion speeds near the coronal base, and these high speeds, in conjuction with a rapid flow tube divergence, may in certain cases produce an increased conductive energy supply to the solar wind. If such an increased conductive energy supply is produced, the need for energy addition above the coronal base is correspondingly reduced. In addition, the high flow speeds at low altitudes make it possible for any required energy addition to occur relatively near the coronal base, so that the need for extended heating of the solar wind may be substantially less than has been suggested in the past. For radiation-driven stellar winds the additional critical points associated with rapid flow tube divergence can lead to supersonic flow much deeper in the stellar atmosphere than is predicted by radial, spherically symmetric flow models, and this might resolve the apparent conflict between radiation-driven wind models and certain observations of Of stars. In two-fluid solar wind models including proton heat addition it is shown that the radial electron temperature profile has a sufficiently important dynamical influence that the accurate treatment of electron energy transport is a primary prerequisite to obtaining quantitatively significant results.