Strong, order of magnitude, depletions in suprathermal electron distribution functions, centered on and roughly symmetric about 90¿ pitch angle, are relatively common on closed field lines threading coronal mass ejection, CME, material in the solar wind. Such depletions are observed within at least portions of most CME events identified in data obtained from the ACE spacecraft. The symmetry of the depletions about 90¿ pitch angle is independent of the width or depth of the depletions or the strengths and angular widths of the field-aligned, counterstreaming beams that characterize closed field lines in the solar wind. We suggest that these symmetric depletions may be largely a consequence of double magnetic connection to the Sun and a relative lack of electron scattering from the counterstreaming beams to large pitch angles.