Neutrino-pair production and annihilation through nucleon-nucleon bremsstrahlung is included in current supernova simulations by rates that are based on the one-pion-exchange approximation. Here we explore the consequences of bremsstrahlung rates based on modern nuclear interactions for proto-neutron star cooling and the corresponding neutrino emission. We find that despite a reduction of the bremsstrahlung emission by a factor of 2–5 in the neutrinospheric region, models with the improved treatment exhibit only ≲5% changes of the neutrino luminosities and an increase of ≲0.7 MeV of the average energies of the radiated neutrino spectra, with the largest effects for the antineutrinos of all flavors and at late times. Overall, the proto-neutron star cooling evolution is slowed down modestly by ≲0.5–1 s.