Distribution of orbital parameters for the globular clusters in our sample. Three globular clusters are not shown in these plots: NGC 3201 and NGC 4590, which have apocentres ~ 30 kpc and large retrograde and prograde motions, respectively (|L_z| > 2000 kpc km s⁻¹), and NGC 5466, which has an apocentre ~50 kpc (given its orbital parameters, it was likely associated with the Sagittarius dwarf, as proposed by Bellazzini et al. 2003). We note the concentration of clusters with small pericentre and apocentre around L_z ~ 0 for Model-3. Such clusters are on box orbits in the barred potential of Model-3, and hence do not conserve L_z, whose time average over the 10 Gyr of integration is approximately zero. The error bars correspond to the 16th and 84th quantiles obtained from the orbit integration using the statistical errors. The effect of the systematic error on the orbits of the globular clusters is found to be negligible and is not shown here.