A metabolic model of height growth and site index is derived from a parametrization of the annual carbon balance of a tree. The parametrization is based on pipe-model theory. Four principal variants of the height-growth model correspond to four combinations of assumptions regarding carbon allocation: (a) the apical shoot is autonomous or (b) it is not; and (A) the specific rate of elongation of a shoot equals that of a woody root or (B) it does not. The bB model is the most general as it includes the aA, bA, and aB models as special cases. If the physiological parameters are constant, then the aA model reduces to the form of the Mitscherlich model and the bA model to the form of a Bertalanffy model. Responses of height growth to year-to-year variation in atmospheric conditions are rendered through adjustments of a subset of the model's parameters, namely, the specific rate of production of carbon substrate and three specific rates of maintenance respiration. As an example, the effect of the increasing atmospheric concentration of CO_{2} on the time-course of tree height of loblolly pine (*Pinus taeda*) is projected over 50-year span from 1986. Site index is predicted to increase and, more importantly, the shape of the site-index curve is predicted to change.