The cosmic ray decreases and interplanetary disturbances observed at 1 AU have been investigated by using some cosmic ray hourly intensities recorded with ground-based monitors at Alert, Deep River, and Mount Washington as well as the interplanetary magnetic field (IMF) and the solar wind plasma bulk speed, density, and temperature in the near-Earth space. We studied a two-step Forbush decrease (FD)-type, with large cosmic ray intensity decreases, on 29--30 September 1978, 24--26 April 1979, 27--28 August 1978, 30 January 1978, 13--15 January 1967, 3--5 January 1978, 28--29 November 1989, and 29--30 December 1989, each of which appears to be produced by the structure within the shock and sheath preceding the interplanetary coronal mass ejection (ICME). There is a sheath upstream of the ICME led by a fast forward shock. The sheath material is slow solar wind that has been swept up by the ICME and is not part of the ICME itself. The sheath material is hot, dense, and turbulent and is most probably produced by the shock. The large IMF variations in the shocked plasma scatter the galactic cosmic rays and thus sweep away the cosmic ray particles. When the IMF variations in the sheath become too feeble (the lull region), the scattering of the galactic cosmic rays ceases, corresponding to the recovery phase of the first step of the FD; the particle scattering resumes when the high IMF variations in the sheath resume and the onset of the second decrease starts. There is a second and rear region inside the interplanetary macrostructure, the ICME/magnetic cloud, where the galactic cosmic rays are also scattered away from the high magnetic field pressure in the magnetic cloud. A data set with fine time resolution (less than an hour) and good statistics is needed to provide an exact timing of the various phenomena.