SYNOPSISThis paper reviews the relationship between tensile strength of native cotton fibers and the various orientation parameters and the true spiral angle. It is concluded that the Hermans crystallite orientation factor and the average angle of crystallite orientation, a,, deduced from it are the best parameters to characterize fiber strength. Moreover, a , represents a closer approximation to the true spiral angle in cotton than do the 50% or 75% X-ray angles. It is recommended that cotton breeders characterize fiber strength and screen genotypes on the basis of the Hermans factor and a, rather than the 40, 50, or 75% X-ray angles.