  The evolution of close-orbit progenitor binaries of double neutron star (DNS)
systems leads to supernova (SN) explosions of ultra-stripped stars. The amount
of SN ejecta mass is very limited from such, more or less, naked metal cores
with envelope masses of only 0.01-0.2 Msun. The combination of little SN ejecta
mass and the associated possibility of small NS kicks is quite important for
the characteristics of the resulting DNS systems left behind. Here, we discuss
theoretical predictions for DNS systems, based on Case BB Roche-lobe overflow
prior to ultra-stripped SNe, and briefly compare with observations.
