Starting from a general statistical model, we investigate the performance of wavelet block thresholding procedures via the maxiset approach under the Lp risk (p>1) for a rate of convergence of the form $n^{-\epsilon}$ (without logarithmic factor). We prove that such procedures can be better in the maxiset sense than the hard thresholding procedures. Moreover, we show that they can be optimal in the minimax sense over Besov balls.