  Close double neutron stars have been observed as Galactic radio pulsars,
while their mergers have been detected as gamma-ray bursts and
gravitational-wave sources. They are believed to have experienced at least one
common-envelope episode during their evolution prior to double neutron star
formation. In the last decades there have been numerous efforts to understand
the details of the common-envelope phase, but its computational modelling
remains challenging. We present and discuss the properties of the donor and the
binary at the onset of the Roche-lobe overflow leading to these common-envelope
episodes as predicted by rapid binary population synthesis models. These
properties can be used as initial conditions for detailed simulations of the
common-envelope phase. There are three distinctive populations, classified by
the evolutionary stage of the donor at the moment of the onset of the
Roche-lobe overflow: giant donors with fully-convective envelopes, cool donors
with partially-convective envelopes, and hot donors with radiative envelopes.
We also estimate that, for standard assumptions, tides would not circularise a
large fraction of these systems by the onset of Roche-lobe overflow. This makes
the study and understanding of eccentric mass-transferring systems relevant for
double neutron star populations.
