In this work, non-recurrent Forbush decreases (FDs) triggered by the passage of shock-driving interplanetary coronal mass ejections (ICMEs) have been analyzed. Fifty-nine ICMEs have been studied, but only 25 % of them were associated to a FD. We find that shock-driving magnetic clouds (MCs) produce deeper FDs than shock-driving ejecta. This fact can be explained regarding the observed growing trends between decreases in neutron monitor (NM) count rate and MC/ejecta speed and its associated rigidity. MCs are faster and have higher associated rigidities than ejecta. Also the deceleration of ICMEs seems to be a cause for producing FDs, as can be inferred from the decreasing trend between NM count rate and deceleration. This probably implies that the interaction between the ICME traveling from the corona to the Earth and the solar wind can play an important role in producing deeper FDs. Finally, we conclude that ejecta without flux rope topology are the ones less effective in unchaining FDs.