  Light dark matter annihilating into electron-positron pairs emits a
significant amount of internal bremsstrahlung that may contribute to the cosmic
gamma-ray background. The amount of emitted gamma-rays depends on the dark
matter clumping factor. Recent calculations indicate that this value should be
of order $10^6-10^7$. That allows us to calculate the expected gamma-ray
background contribution from dark matter annihilation. We find that the light
dark matter model can be ruled out if a constant thermally-averaged cross
section is assumed (s-wave annihilation). For more massive dark matter
candidates like neutralinos, however, cosmic constraints are weaker.
