The singly scattered resonant fluorescent component of the geocoronal Balmer-alpha (H&agr;) emission is obtained by subtracting the multiply scattered component of H&agr;, determined by a radiative-transfer (RT) model, from H&agr; measurements. Exospheric column abundance then follows a straightforward single-scattering calculation. The reality of that abundance depends upon the validity of the model exosphere used by the RT model, upon the validity of the estimated solar Ly-&bgr; flux, and upon the statistical measurement errors. Iterative adjustments of the hydrogen density ([H>) profile input to the RT model, converging to a best fit to H&agr; observations, generate a unique atmosphere best matching model intensity to measured H&agr; brightnesses. Applying this method to ground-based measurements of the geocoronal H&agr; emission made at Arecibo, Puerto Rico, in 1988, we find that the best estimated multiply and singly scattered components of H&agr; are about 85 and 60%, respectively, in excess of the initial model values, while the derived [H> is generally in agreement with the initial model [H> at lower altitudes and about 35% higher than the initial model [H> at higher altitudes. Examination of the iteration technique sensitivity indicates that the neutral temperature prescribed by the MSIS-83 model and the solar Ly-&bgr; flux estimated by a correlation relation are the parameters with the principal impact on the determined [H>. In addition, the examination shows that these parameters impact the RT-calculated intensity components. Because convergence of the iteration technique is insensitive to the initial model guess for most cases, the technique is capable of accurately determining [H> from H&agr; measurements, particularly if the temperature is simultaneously measured and the line center solar Ly-&bgr; flux is known. ¿ American Geophysical Union 1993