Abstract. In this paper, we revisit the constraints obtained by several authors (Reichart et al. 1999;Eke et al. 1998;Henry 2000) Firstly, using the quoted improvements, we re-derive an expression for the X-ray Luminosity Function (XLF), similarly to Reichart et al. (1999), and then we get some constraints to Ωm and n, by using the ROSAT BCS and EMSS samples and maximum-likelihood analysis. Then we re-derive the X-ray Temperature Function (XTF), similarly to Henry (2000), re-obtaining the constraints on Ωm, n, σ8. In the case of both the XLF and the XTF, the changes in the mass function and M-T relation produces an increase in Ωm of 20% and similar results in σ8 and n.