  Using the FitzHugh-Nagumo system in the excitable regime, we investigate the
influence of the L{\'e}vy noise properties on the effect of coherence
resonance. In particular, we demonstrate that the L{\'e}vy noise can be a
constructive or destructive factor providing for enhancement or suppression of
noise-induced coherence. We show that the positive or negative role of the
L{\'e}vy noise impact is dictated by the noise stability index and skewness
parameter. The correlation time and the deviation of interspike intervals used
in this analysis are shown to be maximized or minimized for an appropriate
choice of the noise parameters. Numerical simulations are combined with
experiments on an electronic circuit showing an excellent qualitative
correspondence and proving thereby the robustness of the observed phenomena.
