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.  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 λenv from the binding energy and compare its distribution to typical assumptions that are made in population-synthesis codes. We conclude that λenv 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 αCE. Finally, we discuss accurate existing analytic fits for the envelope binding energy, which make these oversimplified assumptions for λenv, and the use of λenv in general, unnecessary.