Define en(t) = {t/n}. Let dN denote the distance in L2(0, ∞; t-2dt) between the indicator function of [1, ∞[ and the vector space generated by e1,..., eN. A theorem of Báez-Duarte states that the Riemann hypothesis (RH) holds if and only if dN → 0 when N → ∞. Assuming RH, we prove the estimate \begin{eqnarray*} d_N^2 \leq (\log \log N)^{5/2+o(1)}(\log N)^{-1/2}. \end{eqnarray*}