Tools to characterize three important characteristics of turbulence are proposed: Structures-within-structures, intermittent amplitude bursting, and turbulence complexity. These tools are applied to show that the injection of a rf wave into the plasma confined on the Tokamak Chauffage Alfven Bresilien (TCABR) [R. M. O. Galvao, V. Bellintani, Jr., R. D. Bengtson , Plasma Phys. Controlled Fusion 43, A299 (2001)] decreases plasma edge turbulence, although not completely destroy it, by destroying the only two types of time structures found in the data. Both structures present multiscaling spectra, with infinitely many possible scalings. So, according to this analysis, complexity of this turbulence is mainly due to the multiscaling character of the oscillations. (C) 2003 American Institute of Physics.