Magnetic field orientations in the sheaths of ten fast interplanetary coronal mass ejections (ICMEs) that cover the solar longitude range roughly from 20 degrees East to 33 degrees West (as determined from the associated flare or filament disruption) are overlain on the MHD-computed magnetic field pattern showing draping in Earth's magnetosheath. The general draping pattern is evident in the ICME sheath orientations including, most importantly, the east flank where draping causes the greatest distortion of the magnetic field away from the general Parker spiral. Deviations from the general draping pattern are also evident which, we suggest, result from the history of accretion of the inhomogeneous interplanetary magnetic field (IMF) into the ICME sheath over a long stretch of solar wind before arriving at one AU. The profiles of magnetic field intensity between the ICME shock and the nose of the ICME deviate significantly from the corresponding profile in Earth's magnetosheath. The ICME samples are much more irregular and show no general tendency to increase toward the stagnation point. We suggest that again this difference reflects the history of IMF accretion by the ICME sheath. The long stretch of accreted inhomogeneous field (a significant fraction of one AU) can account for the irregularity, and the weakness of the field close to the body possibly reflects a weaker ICME shock closer to the Sun.