  We perform a dispersive theoretical study of the reaction \gamma\gamma\to
pi^0\pi^0 emphasizing the low energy region. The large source of theoretical
uncertainty to calculate the \gamma\gamma\to\pi^0\pi^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 \gamma\gamma\to\pi^0\pi^0 available
one might then distinguish between different parameterizations of the \pi\pi
isoscalar S-wave. We also elaborate on the width of the \sigma resonance to
\gamma\gamma and provide new values.
