A variant of the statistical complexity originally advanced by López-Ruiz et al. [R. López-Ruiz, H.L. Mancini, X. Calbet, Phys. Lett. A 209 (1995) 321], is here used in conjunction with Fisher's information measure so as to explore fine details of chaotic dynamics. As a main result we can easily distinguish between (i) periodicity and chaos or (ii) between distinct chaotic dynamics belonging to different attractors.