We combine accurate measurements at low energies and theoretical calcu
lations at high energies to construct sets of photoionization cross se
ctions of He and H-2 that should be reliable at all energies. We contr
ol the accuracy of the recommended cross section data by ensuring that
they satisfy a range of oscillator strength sum rules. We provide acc
urate analytic formulae for the photoionization cross sections that ha
ve the proper asymptotic form. At high frequencies the cross sections
for H-2 are 2.8 times those for H.