We consider the dispersion of particles in potential vorticity (PV)-conserving flows. Because particle drift is preferentially along the mean PV contours, Lagrangian dispersion is strongly anisotropic. If the mean PV field moreover is spatially variable, as when there is topography, the anisotropy is more clearly visible in the dispersion of displacements along and across the mean PV field itself. We examine several numerical examples of unforced barotropic flows; in all cases, this "projected" dispersion is more anisotropic than that in cartesian (x, y) coordinates. What differs is the rate at which spreading occurs, both along and across contours. The method is applicable to real data, as is illustrated with float data from the deep North Atlantic. The results suggest a preferential spreading along contours of (barotropic) f/H.