We perform a dispersive theoretical study of the reaction gammagammato pi^0pi^0 emphasizing the low energy region. The large source of theoretical uncertainty to calculate the gammagammatopi^0pi^0 total cross section for sqrt{s}gtrsim 0.5 GeV within the dispersive approach is removed. This is accomplished by taking one more subtraction in the dispersion relations, where the extra subtraction constant is fixed by considering new low energy constraints, one of them further refined by taking into consideration the f_0(980) region. This allows us to make sharper predictions for the cross section for sqrt{s}lesssim 0.8 GeV, below the onset of D-wave contributions. In this way, were new more precise data on gammagammatopi^0pi^0 available one might then distinguish between different parameterizations of the pipi isoscalar S-wave. We also elaborate on the width of the sigma resonance to gammagamma and provide new values.
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