Post-kick binary systems in the period-eccentricity plane. Each point represents a detailed binary simulation between a non-degenerate donor star an a NS. The colours indicate the χ² minimum found during the entire evolution of each binary, considering observational constraints on binary parameters (i.e. masses of the NS and its companion, orbital period, and eccentricity; see Table 1). Diamonds represent binaries with matching binary properties to the observed ones. With black squares we show binaries merging just after core collapse due to the kick orientation, while grey squares represent binaries for which numerical problems were encountered and the simulations were not completed. The location of the case of a symmetric kick in this plane is shown with an arrow.