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Steep rise of parton densities in the limit of small parton momentum fraction x poses a challenge for describing the observed energy-dependence of the total and inelastic proton-proton cross sections σtot/inelpp : considering a realistic parton spatial distribution, one obtains a too-strong increase of σtot/inelpp in the limit of very high energies. We discuss various mechanisms which allow one to tame such a rise, paying special attention to the role of parton-parton correlations. In addition, we investigate a potential impact on model predictions for σtotpp, related to dynamical higher twist corrections to parton-production process.