We have measured the thermoelectric power ͑S͒ of high-purity single-walled carbon nanotube mats as a function of temperature at various hydrostatic pressures up to 2.0 GPa. The thermoelectric power is positive, and it increases in a monotonic way with increasing temperature for all pressures. The low-temperature (T Ͻ40 K) linear thermoelectric power is pressure independent and is characteristic for metallic nanotubes. At higher temperatures it is enhanced and though S(T) is linear again above about 100 K it has a nonzero intercept. This enhancement is strongly pressure dependent and is related to the change of the phonon population with hydrostatic pressure.Soon after the discovery of multiwalled carbon nanotubes 1 single-walled carbon nanotubes ͑SWNT͒ were synthesized with catalytic metal particles. 2 SWNT span electronic properties from metals to variable gap semiconductors, depending on the chirality and the diameter of the rolled up graphene sheet. 3 It was immediately realized that metallic tubes represent the ultimate one-dimensional conductor, and they generated considerable interest due to the possible realization of the Luttinger liquid ͑LL͒ behavior in nature. Indeed, conductivity measurements performed on individual nanotubes have shown the canonical power-law behavior of conductance as a function of temperature and voltage. 4 Early thermoelectric power ͑TEP͒ experiments performed on nanotube bundles lead to qualitatively similar results: 5-8 a metallic character due to hole carriers, a knee feature ͑change of slope͒ around 100 K, and preparation dependent magnitude. The observed TEP was associated with intrinsic electronic behavior, and the fact that the nanotube bundles contain both metallic and semiconducting ropes allowed a description of the unusual shape of the S(T) curves in a simple two-band model, using a sufficient number of fitting parameters. It was also realized that in the high-temperature range the thermoelectric power is significantly larger than expected for bundles constituted predominantly of metallic ropes. 5 Since SWNT's may be contaminated by magnetic impurities coming from the catalysts ͑Fe, Ni, Co͒ needed for their growth, the high value of the TEP above 100 K questions its intrinsic origin. The influence of the magnetic impurities has clearly been experimentally demonstrated: 9 in the presence of transition-metal impurities the thermopower has a strong peak, just around 100 K. This peak was associated with the Kondo scattering of conduction electrons on the impurity spins. The enhancement of the TEP could be largely, albeit not completely, removed by iodine neutralization. 9 A nonintrinsic, residual ''Kondo term'' may arise from magnetic impurities trapped on the body of the nanotubes, even in the case of nominally pure samples.The change of sign of the thermoelectric power upon degassing also raised the possibility of a nonintrinsic process. 10 The conductivity of doped semiconducting tubes can be as high as that of the metallic ones and the overall thermopower may be determin...