Excitonic spectra of ultra-thin free plates of hexagonal CdSe in magnetic fields up to 8T at T= 1.7K have been studied. Fan diagrams were interpreted as containing both "weak-field" (Zeeman splitting and diamagnetic shift) and "strong-field" (inter-Landau-level transitions) information. Two sets, "bare" and "polaron", of the wurtzite CdSe band parameters were calculated in the frame of quasi-cubic approximation, using best possibilities of these two regimes of the excitonic magnetooptics. The obtained parameters are: electron-effective mass m(e) = 0.125/0.116m(0), Luttinger parameters gamma(1) = 1.5/1.7 and gamma = 0.3/0.4 for polaron/bare hole, magnetic Luttinger parameter kappa = - 0.63 and electron effective g-factor g(e) = 0.7.