How rapidly do neutron stars spin at birth?

We have studied the X-ray properties of ageing historical core-collapse supernovae in nearby galaxies, using archival data from Chandra, XMM-Newton and Swift. We found possible evidence of a young X-ray pulsar in SN 1968D and in few other sources, but none more luminous than ~ a few 10^{37} erg/s. We compared the observational limits to the X-ray pulsar luminosity distribution with the results of Monte Carlo simulations for a range of birth parameters. We conclude that a pulsar population dominated by periods <~ 40 ms at birth is ruled out by the data.