  Recent neutron star surface observations corroborate a long-standing theory
that neutron stars may be accelerated over extended periods after their birth.
We analyze how these prolonged rocket-like accelerations, combined with rapid
birth kicks, impact binary orbits. We find that even a small contribution of
rocket kicks combined with instantaneous natal kicks can allow binaries to
reach period--eccentricity combinations unattainable in standard binary
evolution models. We propose these kick + rocket combinations as a new channel
to form wide low-eccentricity neutron star binaries such as Gaia NS1, as well
as inducing stellar mergers months to years after a supernova to cause peculiar
high-energy transients.
