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The optimization of the electronic conduction of carbon nanotube polymer composites is studied by tuning the radial geometry of the carbon nanotubes in a compression cycle. We have investigated the structural evolution of multi-walled carbon nanotubes in a polyamide matrix as a function of applied high pressure. Combining high resolution electron microscopy and small angle neutron scattering experiments, we conclude that the nanotube radial cross-section is irreversibly deformed following applied pressures up to 5 GPa. Studying highly percolated composites we observe that the sample resistivity drastically decreases with pressure up to about 2 GPa with no further change up to the maximum 5 GPa applied pressure. An important hysteresis is observed upon decompression which leads to an enhanced electrical conductivity of the composite in all the studied compression cycles with maximum pressures ranging from 1 to 5 GPa. Modelling the radial collapse of single-walled carbon nanotubes shows that the modified radial geometry can considerably improve the electronic transport properties in contacted carbon nanotube junctions. Our results open opportunities for engineering nanotube composites by controlling the radial collapse.