A form for the point-source gamma-ray energy absorption buildup function valid for a material in the energy range where it is essentially a Compton scatterer is suggested as a modification of the asymptotic forms derived by U. Fano. Its parameters are evaluated by means of an energy equilibrium condition and a fit to experimental data. The results are compared with those obtained by other methods, and an application to the problem of uniformly and continuously distributed point sources is discussed.