We model the recently published kinematic data set for Leo I dwarf spheroidal (dSph) galaxy by fitting the solutions of the Jeans equations to the velocity dispersion and kurtosis profiles measured from the data. We demonstrate that when the sample is cleaned of interlopers the data are consistent with the assumption that mass follows light and isotropic stellar orbits with no need for an extended dark matter halo. Our interloper removal scheme does not clean the data of contamination completely, as demonstrated by the rotation curve of Leo I. When moving away from the centre of the dwarf, the rotation appears to be reversed. We interpret this behaviour using the results of an N-body simulation of a dwarf galaxy possessing some intrinsic rotation, orbiting in the Milky Way potential and show that it can be reproduced if the galaxy is viewed almost along the tidal tails so that the leading (background) tail contaminates the western part of Leo I while the trailing (foreground) tail the eastern one. We show that this configuration leads to a symmetric and Gaussian distribution of line-of-sight velocities. The simulation is also applied to test our modelling method on mock data sets. We demonstrate that when the data are cleaned of interlopers and the fourth velocity moment is used the true parameters of the dwarf are typically within 1σ errors of the best-fitting parameters. Restricting the fitting to the inner part of Leo I our best estimate for the anisotropy is β=−0.2+0.3−0.4 and the total mass M= (4.5 ± 0.7) × 107 M⊙ . The mass-to-light ratio (M/L) including the errors in mass, brightness and distance is M/LV= 8.2 ± 4.5 solar units.