The classification of galaxy clusters according to their X-ray appearance is a powerful tool to discriminate between regular clusters (associated to relaxed objects) and disturbed ones (linked to dynamically active systems). The compilation of the two subsamples is a necessary step both for cosmological studies -oriented towards spherical and virialized systems-and for astrophysical investigations -focused on phenomena typically present in highly disturbed galaxy clusters such as turbulence, particle re-acceleration, magneto-astrophysics .In this paper, we review several morphological parameters: asymmetry and fluctuation of the X-ray surface brightness, hardness ratios, X-ray surface-brightness concentration, centroid shift, and third-order power ratio. We test them against 60 Chandra-like images obtained from hydrodynamical simulations through the X-ray Map Simulator and visually classified as regular and disturbed.The best performances are registered when the parameters are computed using the largest possible region (either within R 500 or 1000 kpc). The best indicators are the third-order power ratio, the asymmetry parameter, and the X-ray-surface-brightness concentration. All their combinations offer an efficient way to distinguish between the two morphological classes achieving values of purity extremely close to 1. A new parameter, M, is defined. It combines the strengths of the aforementioned indicators and, therefore, resulted to be the most effective parameter analyzed.