With the plethora of detailed results from heliospheric missions and at the advent of the first mission dedicated IBEX, we have entered the era of precision heliospheric studies. Interpretation of these data require precision modeling, with second-or
der effects quantitatively taken into account. We study the influence of the non-flat shape of the solar Ly-alpha line on the distribution of neutral interstellar H in the inner heliosphere. Based on available data, we (i) construct a model of evolution for the solar Ly-alpha line profile with solar activity, (ii) modify an existing test-particle code used to calculate the distribution of neutral interstellar H in the inner heliosphere so that it takes the dependence of radiation pressure on radial velocity into account, and (iii) compare the results of the old and new version. Discrepancies between the classical and Doppler models appear between ~5 and ~3 AU and increase towards the Sun from a few percent to a factor of 1.5 at 1 AU. The classical model overestimates the density everywhere except for a ~60-degr cone around the downwind direction, where a density deficit appears. The magnitude of the discrepancies appreciably depends on the phase of the solar cycle, but only weakly on the parameters of the gas at the termination shock. For in situ measurements of neutral atoms performed at ~1 AU, the Doppler correction will need to be taken into account, because the modifications include both the magnitude and direction of the local flux by a few km/s and degrees, respectively, which, when unaccounted for, would introduce an error of a few km/s and degrees in determination of the magnitude and direction of the bulk velocity vector at the termination shock.
