The greatest Leonid meteor storms since the late eighteenth century are generally regarded as being those of 1833 and 1966. They were evidently due to dense meteoroid concentrations within the Leonid stream. At those times, the orbit of Comet 55P/Tempel-Tuttle was significantly nearer that of the Earth than at most perihelion returns, but still some tens of Earth radii away. Significantly reducing this miss distance can be critical for producing a storm. Evaluation of differential gravitational perturbations, comparing meteoroids with the comet, shows that, in 1833 and 1966 respectively, the Earth passed through meteoroid trails generated at the 1800 and 1899 returns.