  We present basic properties of primary stars that initiate a common envelope
(CE) in a binary, while on the giant branch. We use the population-synthesis
code described in Politano et al. (2010) and follow the evolution of a
population of binary stars up to the point where the primary fills its Roche
lobe and initiates a CE. We then collect the properties of each system, in
particular the donor mass and the binding energy of the donor's envelope, which
are important for the treatment of a CE. We find that for most CEs, the donor
mass is sufficiently low to define the core-envelope boundary reasonably well.
We compute the envelope-structure parameter {\lambda_\mathrm{env}} from the
binding energy and compare its distribution to typical assumptions that are
made in population-synthesis codes. We conclude that {\lambda_\mathrm{env}}
varies appreciably and that the assumption of a constant value for this
parameter results in typical errors of 20--50%. In addition, such an assumption
may well result in the implicit assumption of unintended and/or unphysical
values for the CE parameter {\alpha_\mathrm{CE}}. Finally, we discuss accurate
existing analytic fits for the envelope binding energy, which make these
oversimplified assumptions for {\lambda_\mathrm{env}}, and the use of
{\lambda_\mathrm{env}} in general, unnecessary.
