We investigate the physical parameters controlling the low energy screening in carbon nanotubes via electron energy loss spectroscopy and inelastic x-ray scattering. Two plasmon-like features are observed, one near 9 eV (the so-called pi plasmon) and one near 20 eV (the so-called pi+sigma plasmon). At large nanotube diameters, the pi+sigma plasmon energies are found to depend exclusively on the number of walls and not on the radius or chiral vector. The observed shift indicates a change in the strength of the screening and in the effective interaction at inter-atomic distances, and thus this result suggests a mechanism for tuning the properties of the nanotube.