The integrated optical depth (up to z= 60) due to Thomson scattering, τ, as a function of the number of χ² degrees of freedom considering different evolutions for the clumping factor parametrized by β= 2 (solid line), β= 1 (dashed line) and β= 0 (dotted line) and a reionization model with ε_II= 0. The horizontal stripe represents the range of τ allowed by the WMAP three-year data (at 68 per cent confidence level).