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ABSTRACT Current prescriptions for supernova natal kicks in rapid binary population synthesis simulations are based on fits of simple functions to single pulsar velocity data. We explore a new parametrization of natal kicks received by neutron stars in isolated and binary systems developed by Mandel & Müller, which is based on 1D models and 3D supernova simulations, and accounts for the physical correlations between progenitor properties, remnant mass, and the kick velocity. We constrain two free parameters in this model using very long baseline interferometry velocity measurements of Galactic single pulsars. We find that the inferred values of natal kick parameters do not differ significantly between single and binary evolution scenarios. The best-fitting values of these parameters are $$v$$ns = 520 km s−1 for the scaling prefactor for neutron star kicks, and σns = 0.3 for the fractional stochastic scatter in the kick velocities.