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 M _ { \odot } .
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 .