  Counterstreaming beams of electrons are ubiquitous in coronal mass ejections
(CMEs) - although their existence is not unanimously accepted as a necessary
and/or sufficient signature of these events. We continue the investigations of
a high-latitude CME registered by the \emph{Ulysses} spacecraft on January
18\,--\,19, 2002 (Dumitrache, Popescu, and Oncica, Solar Phys. {\bf 272}, 137,
2011), by surveying the solar wind electron distributions associated with this
event. The temporal-evolution of the pitch-angle distributions reveal
populations of electrons distinguishable through their anisotropy, with clear
signatures of i) electron strahls, ii) counter-streaming in the magnetic clouds
and their precursors, and iii) unidirectional in the fast wind preceding the
CME. The analysis of the counter-streams inside the CME allows us to elucidate
the complexity of the magnetic-cloud structures embeded in the CME and to
refine the borders of the event. Identifying such strahls in CMEs, which
preserve properties of the low $\beta < 1$ coronal plasma, gives more support
to the hypothesis that these populations are remnants of the hot coronal
electrons that escape from the electrostatic potential of the Sun into the
heliosphere.
